Foreign Secretary Mr Hunt wrote in a newspaper article that the Conservatives would be committing ‘political suicide’ if they try to force a cliff-edge exit.
But Miss McVey immediately fired back, saying: ‘Political suicide actually lies in not having a clean break from the EU and not leaving on October 31.’
The two MPs are among nine Conservatives who have thrown their hats in the ring to replace Theresa May at Number 10.
Jeremy Hunt (left) has clashed with Esther McVey (right) over the prospect of a No Deal Brexit in the first sign of open conflict between Tory leadership rivals
Mr Hunt had written in the Daily Telegraph that pursuing No Deal was ‘political suicide, that would delight Nigel Farage and probably put Jeremy Corbyn in No 10 by Christmas’.
If he became Prime Minister he would try to renegotiate a Brexit deal with Brussels, saying he would ‘go to them with a shared problem and there is a chance of a shared solution’.
His comments put him at odds with many Tory candidates who yesterday lined up to pledge they would finally take the country out of the European Union after the Tories suffered their worst election result in 200 years.
Tory leadership contender Matt Hancock (pictured) has declared it is ‘mission critical’ for the party to deliver Brexit before the next general election
Boris Johnson, the favourite to succeed Theresa May, tweeted: ‘The message is clear. It is time for us to deliver Brexit and set out our positive plans for the country.’
Sajid Javid, who entered the race yesterday, said getting the country out of the EU would be his ‘first and foremost’ priority.
The European Parliament election results saw the Tories slump to fifth place with just four MEPs.
Also writing in today’s Telegraph, Nigel Farage said the success for his Brexit Party was ‘only the start’, warning that his party was ready to stand in the general election ‘whenever it comes’.
‘It took the Labour Party 45 years to win the popular vote in a national election. The Brexit Party has done it in 45 days,’ he boasted.
Miss McVey earlier declared it was no longer possible to find a Brexit a plan ‘to bring people together’ as she argued that leaving without a deal is the only thing that ‘will wash now’.
The former Work and Pensions Secretary quit the Cabinet in November 2018 in protest at Theresa May’s Brexit deal.
The Tatton MP said the Conservative Party needed a leader who ‘believes in Brexit’, and had ‘belief in the opportunities’ it could bring.
But Miss McVey said that Mrs May’s departure should be handled in a ‘dignified and graceful’ way.
This map shows by council that the Brexit Party have topped polls in almost everywhere in England and Wales. The Tories have not come first in any council areas
Tory leadership contenders including (l-r) Andrea Leadsom and Dominic Raab were among those to issue dire warnings for the Conservative Party if it cannot sort out Brexit fast
‘We all know Theresa May is dutiful,’ she said. ‘She has worked for public service for many years.’
Mr Hunt chose to play up his record as a businessman as he launched his campaign, saying: ‘If I was prime minister, I’d be the first prime minister in living memory who has been an entrepreneur by background.
‘Doing deals is my bread and butter as someone who has set up their own business.’
Mr Hunt’s emphasis on his entrepreneurial past is being seen as swipe at Mr Johnson who reportedly once said ‘f*** business’ in relation to Brexit.
Fellow contender Matt Hancock has declared it is ‘mission critical’ for the party to deliver Brexit before the next general election.
The Health Secretary said the party was under attack ‘on two sides’ as Nigel Farage humiliated the party while Conservative candidates also fell behind the pro-Europe Liberal Democrats.
Writing for the Daily Mail, Mr Hancock warned that ‘Tory voters who supported Remain and younger voters who share our values are being hoovered up by the Lib Dems in growing numbers’.
He said said the party risked losing seats it had won from the Lib Dems in places such as the South West if it failed to ‘hold our nerve’ and pursued a No Deal Brexit instead.
The Brexit Party won the most seats in the election last Thursday, followed by the Lib Dems
This chart shows the parties’ respective share of the vote, with Labour third and the Tories fifth
The Conservatives suffered a humiliating 14.9 per cent loss in their 2014 vote share in last night’s European election results
The Conservative vote share slumped to around 9 per cent – thought to be its lowest in a national election since 1834 when the party took on its current name
So who will replace Theresa? Bookies’ favourite Boris is ODDS-ON to take May’s crown as a DOZEN former ministers and backbenchers enter the race to be PM
Boris Johnson is favourite to replace Theresa May’s after her decision to resign on June 7 fired the official starting gun on the race to succeed her.
The long-term favourite has roared into a commanding lead to win the vote to take over as Tory leader and become the Prime Minister who will be faced with delivering Brexit.
But the field in the contest due to take place in June and July is likely to be wide, with more than a dozen ministers, former ministers and backbenchers believed to be ready to run.
Eight MPs have now said they will run: Mr Johnson, Dominic Raab, Rory Stewart, Jeremy Hunt, Andrea Leadsom, Michael Gove, Matt Hancock and Esther McVey.
Sajid Javid is also believed to be considering a run, alongside outsiders including hardline Brexiteer Steve Baker and even Sir Graham Brady, the chairman of the backbench 1922 Committee.
Here we look at the main runners and riders, with their odds with Ladbrokes and how they voted in the 2016 referendum:
Theresa May broke down in tears as she announced she would step down as party leader on June 7, sparking a leadership battle in June and July
Mr Johnson, the former foreign secretary, has long been the bookies’ favourite to replace Theresa May
Boris Johnson: The long-running thorn in May’s side who has recently had a ‘prime ministerial’ makeover
Boris Johnson split from his wife Marina and is in a relationship with former Conservative staffer Carrie Symonds
- Former foreign secretary and mayor of London
- Voted leave and has become an increasingly hardline Brexiteer
- As likely to make headlines over his private life
- Has recently lost a lot of weight and smartened up his appearance
- Leadership odds 6/4
The former foreign secretary, 54, who quit last July and has been tacitly campaigning for the leadership ever since. He finally went public last week to confirm he would run.
Never far from the limelight the father-of-four recently split from his wife Marina and is in a relationship with former Conservative staffer Carrie Symonds, 20 years his junior.
As an increasingly hawkish Brexiteer who says we should not be afraid of leaving without a deal he is hugely popular with the party faithful.
At the start of the year he underwent what might be deemed a ‘prime ministerial’ makeover, losing weight and taming his unruly mop of blonde hair.
Popular with the rank-and-file membership he has less fans in the parliamentary party and may face a concerted campaign to block his succession.
Dominic Raab: Brexiteer who quit rather than back Mrs May’s deal
Dominic Raab has become a cheerleader for a hard Brexit since stepping down as Brexit secretary in November
- Shortlived Brexit secretary last year, replacing David Davis in the hot seat
- But walked in November over terms agreed by PM
- Voted for Brexit in 2016
- Leadership odds 4/1
Mr Raab, 45, is another Vote Leave member who became Brexit secretary after David Davis quit alongside Mr Johnson last July over the Chequers plan.
But he lasted just a matter of months before he too jumped ship, saying he could not accept the terms of the deal done by the Prime Minister.
Like Mr Johnson and Mr Davis he has become an increasingly hardline Brexiteer, sharing a platform with the DUP’s Arlene Foster and suggesting we should not be afraid of a no-deal Brexit.
The Esher and Walton MP’s decision to quit in November, boosted his popularity with party members but he lacks the wider popular appeal of Mr Johnson.
And like Mr Johnson he might benefit from having quit the Cabinet at an earlier stage and dissociating himself with the dying days of the May administration.
His odds have shortened as he is seen as possibly a more palatable alternative Brexiteer to Boris by MPs seeking to block Mr Johnson’s run.
He recently posed for a glossy photoshoot with wife Erika at their Surrey home.
Michael Gove: The boomerang cabinet minister with a Machiavellian reputation
Michael Gove has made a remarkable political comeback after being sacked by Theresa May in 2016
- Leading Vote Leave figure in 2016 who now backs PM’s Brexit deal
- Former journalist, 51, who stood for leadership in 2016
- Was sacked as education minister by Theresa May
- Later returned as Environment Minister
- Leadship odds 5/1
A Brexiteer with a Machiavellian reputation after the 2016 leadership campaign in which he first supported Boris Johnson for the leadership and then stood against him, to their mutual disadvantage.
The former education secretary – sacked by Mrs May – was rehabilitated to become a right-on environment secretary – complete with reusable coffee cups and a strong line on food standards after Brexit.
Despite being a former lead figure in the Vote Leave campaign alongside Mr Johnson the former journalist and MP for Surrey Heath has swung behind Mrs May’s Brexit deal – which might count against him.
Supports leaving with a deal and while he says a No deal Brexit would come with ‘problems’ he believes the country could get through it.
Seen as one of the Cabinet’s strongest political thinkers and having stood once it is unthinkable that he would not stand again.
He will again be pitched against Mr Johnson in a battle for Brexiteer votes.
Andrea Leadsom: May’s former rival who finally decided she could take no more
Ms Leadsom (pictured today) quit the cabinet yesterday. She is a Brexiteer who frequently clashed with Speaker John Bercow
- The Commons’ Leader challenged May in 2016
- Voted for Brexit
- Hosted Brexiteer ‘pizza party’ plot last year
- Increasingly outspoken Brexiteer
- Leadership odds 12/1
The former Commons’ Leader piled pressure on the Prime Minister by announcing her own resignation from the Cabinet on Wednesday.
In a parting blast, the Commons Leader said she could not stomach the latest version of Mrs May’s Brexit deal, with its offer of a second referendum.
In a brutal resignation letter she said: ‘I no longer believe that our approach will deliver on the referendum result.’
It was the final act by an MP whose departure had seemingly been on the cards for months.
Mrs Leadsom, a mother of three, stood against Mrs May for the party leadership in 2016 before conceding defeat before it was put to a vote of MPs.
As collective responsibility largely broke down among ministers she became an increasingly vocal and clear Brexiteer voice in the Cabinet along line similar lines to Mr Johnson and Mr Raab.
She was the host of a Brexiteer ‘pizza party’ in Parliament that included Michael Gove and Liz Truss as the vying wings of the Cabinet plotted to shape the Brexit deal they wanted.
In her role as Commons’ Leader she frequently clashes with Speaker John Bercow over issues including bullying in Parliament.
It is something that will do her no harm among the Tory backbenches where he is widely loathed.
Jeremy Hunt: Remainer turned Brexiteer unity candidate who wants to heal the party
Jeremy Hunt, a born-again Brexiteer after supporting Remain, toured Africa last month with wife Lucia
- The Foreign Secretary voted Remain
- But has become an increasingly vocal Brexiteer
- Former health secretary backs May’s deal
- Has approached ministers about running as a unity candidate
- Leadership odds 12/1
The Foreign Secretary who has undergone a Damascene conversion to the Brexit cause and is seen as a safe if uninspiring pair of hands.
The 52-year-old South West Surrey MP has reportedly been selling himself to colleagues as a unity candidate who can bring together the fractious Tory factions into something approaching a cohesive party.
A long-serving health secretary, the father-of three replaced Mr Johnson as the UK’s top diplomat and has won some plaudits over issues like the imprisonment of British mother Nazanin Zaghari-Ratcliffe in Iran.
But critics point to tub-thumpingly comparing the EU to the USSR at the party conference last year – which was very badly received in Brussels – and a gaffe in which he referred to his Chinese wife as ‘Japanese’ as a reception in China.
Last month he went on a tour of Africa in which his Chinese wife Lucia made a major appearance, after he gaffed by forgetting her nationality.
Last week he called for a ‘decisive’ hike in defence spending to see off the rising threat from Russia and China – in a speech seen as a clear signal of his leadership ambitions.
Speaking at the Lord Mayor’s Banquet Mansion House in the City of London, he said the UK’s hard power must be strengthened, with billions more spent on new capabilities to tackle drones and cyber attacks.
Rory Stewart: Remainer rising star and friend of royals who is not short of confidence
The father of two is married to Shoshana, whom he first met when they worked together in Iraq and she was already married
- Penrith MP, 46, is a former tutor to the Dukes of Cambridge and Sussex
- Old Etonian ex-soldier worked for Foreign Office in Iraq and set up a charity for the Prince of Wale sin Afghanistan
- Voted for Remain and still backs a soft Brexit
- Leadership odds 16/1
The former prisons minister who once vowed to quit if they did not improve within a year declared his candidacy almost as soon as he was promoted to the Cabinet.
He stepped up to International Development Secretary earlier this month to replace Ms Mordaunt and days later declared he will run for the Tory leadership.
The Theresa May loyalist praised the PM for her ‘courageous effort’ to pass her Brexit deal but admitted he would throw his hat in the ring when she steps down.
Urging his party not to ‘try to outdo Nigel Farage’, the development secretary said the Tories should ‘stretch all the way from Ken Clarke to Jacob Rees-Mogg’.
He also lashed out at Mr Johnson at the weekend, saying he would not serve under a No Deal-supporting PM.
The Old Etonian former tutor to the Dukes of Cambridge and Sussex previously worked for the Foreign Office in Iraq and set up a charity for the Prince of Wales in Afghanistan.
He has also written several books about walking.
The father of two is married to Shoshana, whom he first met when they worked together in Iraq and she was already married.
Seen as highly intelligent his staunch Remainer and soft Brexit credentials look likely to count against him in a race set to be dominated by the Brexiteer wing of the party.
Matt Hancock: Waffle-loving health secretary who wants Tories to choose a younger leader
Then culture secretary Mr Hancock with his wife Martha at the 2018 NME Awards
- The youngest front-runner at 40
- A Remainer who now backs Theresa May’s Brexit deal
- He wants the party to look to the future and attract younger voters
- Leadership odds 20/1
The Health Secretary is, like his predecessor Jeremy Hunt, seen as something of a unity candidate.
The 40-year-old father of three is seen as a safe pair of hands despite a few teething problems in his latest Cabinet role.
Last year he was accused of breaking ethics rules after he praised a private health firm app in a newspaper article sponsored by its maker.
But he has since made some hard-hitting interventions in areas like the impact of social media on health.
Last month he joined Ms Mordaunt in backing the Generation Why? report showing that the Tories needed to become more relevant to younger voters.
He called on the party to change its ‘tone’ towards modern Britain or face Jeremy Corbyn as prime minister, in a speech widely seen as setting out his leadership credentials.
This week he showed his human side by unashamedly chomping calorific stroopwafels before a TV broadcast, saying he people should enjoy things in moderation.
Penny Mordaunt: The highly regarded Brexiteer promoted to take on defence
Ms Mordaunt is an outsider for the leadership but is highly thought of in Brexiteer groups
- The MP for Portsmouth North is a Royal Navy reservist
- Highly regarded in Brexiteer circles
- She has been consistently tipped to quit over Brexit but remains in the Cabinet
- Once appeared in a swimsuit in a reality TV show
- Leadership odds 25/1
The new Defence Secretary – the first woman ever to hold the post – is highly regarded in Brexiteer circles.
The Royal Navy reservist, 46, carved out a niche at International Development with some eye-catching suggests about changing how the UK spends disperses aid cash.
She has become an increasingly serious politician after initially being seen as lighthearted when she appeared in a swimsuit in ITV reality TV show Splash!
She was promoted earlier this month to replace Gavin Williamson when he was sacked for leaking details from a confidential meeting about Huawei.
Over the preceding few months she was at the heart of persistent rumours that she would be the next Brexit-supporting minister out the door over Brexit.
She has yet to announce she is running but last month she backed a thinktank report saying the party needed to attract new voters.
She said the party needed to ‘act swiftly’ to win over the younger generations who were turning away from the centre-Right in ‘unprecedented’ numbers.
On Wednesday, after other Cabinet Brexiteers including Andrea Leadsom were notable by their absence during Prime Minister’s Questions, she remained at her post. It remains to be seen whether this loyalty will count for or against her.
Sajid Javid: Remainer star who has run into trouble over knife crime and refugees
Sajid Javid, pictured with his wife Laura, has seen his stock take a hit over the knife crime crisis and migrants crossing the English Channel in small boats
- The most senior cabinet contender
- Voted Remain but wants to see Brexit delivered
- Faced criticism as Home Secretary
- But has taken a hard line on Shamima Begum case
- Leadership odds 33/1
The Home Secretary, a Remainer who wants to see Brexit delivered, was the leading candidate from inside the Cabinet to replace Mrs May.
After replacing Amber Rudd last year he consciously put clear ground between himself and the Prime Minister on issues like caps on skilled migrants after Brexit.
But his credentials have taken a hit recently. He finds himself facing ongoing criticism of his handling of the knife crime crisis affecting UK cities, which sparked a Cabinet row over funding for police.
He also lost face over his handling of the influx of migrants crossing the English Channel in January, being seen to move slowly in realising the scale of the problem.
But more recently the 49-year-old Bromsgove MP has made a serious of hardline decision designed to go down well with Tory voters.
Most notably they have included moving to deprive London teenager turned Jihadi bride Shamima Begum, 19, of her British citizenship, after she was discovered among former Islamic State members in a Syrian refugee camp.
Steve Baker: Brexiteer ‘Spartan’ and self-styled ‘hardman’ who refused to budge over Brexit
Brexit ‘hardman’ Steve Baker has previously threatened to leave the Tories over Brexit
- Former Brexit minister who resigned last year
- A member of the European Research Group which has has opposed Theresa May’s deal in every vote
- Threatened to quit the Tories over Brexit earlier this year
- Leadership odds 33/1
The High Wycombe MP, 47, is a Brexit purist who has never backed Theresa May’s deal.
In March he even threatened to quit the party over the issue, saying: ‘We’ve been put in this place by people whose addiction to power without responsibility has led them to put the choice of No Brexit or this deal.
‘I may yet resign the whip than be part of this.’
The married former RAF engineer officer described himself as a ‘hardman’ in a TV interview this year, only to be shown shortly afterwards in a documentary crying in his office.
Today he told the BBC: ‘There is no point shying away from it, people have been asking me to stand. I have had a degree of support from across the country that I could never have foreseen.
‘I have also had some MPs asking me to stand but I need to face up to the challenge of taking a decision on whether I should do it.’
Sir Graham Brady: Backbench kingmaker with an eye on the throne?
The chairman of the influential 1922 Committee of backbench MPs has played a key but neutral role in the downfall of Theresa May
- Quit today as chairman of the 1922 Committee of backbench MPs
- He went into Downing Street today to tell Mrs May time was up
- But his name was oddly missing from a later statement on leadership
- Leadership odds 50/1
As chairman of the influential 1922 Committee of backbench MPs he has played a key but neutral role in the downfall of Theresa May.
But he quit that post after nine years today ahead o a possible run for the top job.
Despite being a Brexiteer he has been an independent arbiter, overseeing the no-confidence vote Mrs May survived in December and reportedly opposing attempts to change the rules to dethrone her early.
The married father of two has held several meetings with the PM in recent weeks as the mutiny against her grew and this morning saw her in Downing Street where he told her that her time was up.
But his name was conspicuously absent from a later Conservative Party statement about how the leadership election would happen.
He told the Press Association: ‘I have been approached by a number of colleagues across the party both inside and outside Parliament asking me to put myself forward as a candidate.
‘Therefore I have taken the decision to stand down from the position of chairman of the 1922 Committee in order to ensure a fair and transparent election process.
‘I am considering the approaches I have received and will make a further statement in due course.’
His Brexiteer credentials and honourable display as Mrs May was brought down will count in his favour but he lacks frontbench experience, having a sole three-year stint as a shadow Europe minister 15 years ago on his CV.
Esther McVey: Former TV presenter and minister who quit Government over Brexit
The former television journalist, is engaged to fellow Tory backbench Brexiteer Philip Davies, 47
- The 51-year-old was Work and Pensions Secretary until quitting in November
- She was a presenter on GMTV before entering politics
- Is engaged to fellow Tory MP Philip Davies
- This week launched a ‘blue collar Conservatism’ project
- Leadership odds 50/1
The former Work and Pensions Secretary declared her leadership bid last month and has set out a stall as a right-wing blue-collar candidate from a working class Liverpudlian background.
The former television journalist, is engaged to fellow Tory backbench Brexiteer Philip Davies, 47, having previously had a romance with ex-minister Ed Vaizey. She has no children.
This week she set out her leadership pitch by calling for the party to use £7billion of foreign aid cash on buckling British police forces and schools.
Launching a ‘blue collar conservatism’ campaign the Brexiteer MP, 51, said her party had ‘lost the trust’ of working people by failing to leave the EU already and must pursue ‘radical conservative agendas’ to win it back’.
She said that keeping cash in the UK that is currently sent abroad would allow an increase of £4billion in spending on schools and £3billion for police, which are both demanding more money.And she declined to rule out doing a post-election deal with Nigel Farage – but said that if the Tories got the UK out it would mean that his Brexit Party would have no reason to exist. Speaking in Westminster she reiterated her call for the next party leader to be ‘someone who believes in Brexit’ – a dig at Mrs May, who supported the Remain campaign in 2016.