The PM will also host other union leaders, including the GMB’s General Secretary Tim Roach, Unison’s Dave Prentis, and Frances O Grady from the TUC, for the meeting on Thursday.
It will be the first time that Mrs May has met Mr McCluskey – the boss of Britain’s biggest union, a close ally of Jeremy Corbyn and one of the PM’s fiercest critics.
The PM is laying on the trade union charm offensive after her Brexit plan was rejected by 432 to 202 votes – the biggest defeat ever inflicted on a British PM.
Mrs May held calls with the union chiefs less than a fortnight ago – the first time she has ever picked up the phone to them.
Theresa May (pictured outside No10 yesterday) is launching a trade union charm offensive to try to win backing for her Brexit deal
Unite boss Len McCluskey (pictured left) and GMB General Secretary Tim Roach (pictured right) have been invited to Brexit talks at No10 on Thursday
And yesterday she signalled that she is would be prepared to give union chiefs a say in the next stage of Brexit talks as she desperately scrambles to try to win more support.
What is Tuesday’s Plan B vote and what will it mean?
What is happening?
Because Theresa May’s Brexit deal was defeated, the law says she must tell Parliament what her Plan B is.
This has to be done in a motion to the Commons, which will be voted on by MPs next Tuesday night.
That motion can be re-written by MPs if they table amendments and win a vote in favour of them.
Some amendments have already been tabled and MPs can keep producing them until Monday night.
What does May’s plan say?
It promises more cross-party working, renews commitments to protecting workers’ rights after Brexit and says the PM will ask Brussels for more concessions on the backstop.
It it based on the current deal that was crushed by 230 votes last week.
What do the main amendments say?
Jeremy Corbyn’s amendment says Parliament should vote on ‘options’ including a renegotiation of the deal to get a permanent customs union and for a second referendum.
A cross party amendment from Yvette Cooper and Nicky Morgan seeks to block no deal by giving time to a draft law that would require the Government to delay Brexit if a deal has not been agreed by February 26. It upturns normal convention by putting a backbench MP’s Bill ahead of Government plans.
An amendment from Tory rebel Dominic Grieve seeks to set up weekly debates that would mean regular votes on what to do in the absence a deal. His amendments sets aside six named days for the debates – including as late as March 26.
What would the vote do?
Legally nothing – but if the Commons votes in favour of a clear way forward by a majority it will be a major political signal of what might happen.
Is it a new ‘meaningful vote’ that can approve May’s deal?
No. At some point, the PM will have to stage a repeat of last week’s vote to get explicit approval from MPs to go ahead with her deal if she wants it to survive.
Addressing MPs yesterday on her so-called Brexit Plan B, Mrs May said: ‘We will reach out beyond this House and engage more deeply with businesses, civil society and trade unions.’
Mrs May is this afternoon holding calls with business groups including the CBI, the Federation of Small Businesses, and the Institute of Directors.
After suffering a humiliating defeat on her Brexit deal, the PM is desperately trying to garner more support for her Brexit plans.
But she was mocked by Labour and Remainer MPs last night after she unveiled her Brexit Plan B – and it looked remarkably similar to her Plan A.
She again vowed to oppose a second referendum or any delay to Brexit, and instead pledged to go back to Brussels and try to get fresh concessions on the hated Irish backstop.
Her words won plaudits from the DUP and Brexiteers, but Tory Remainers and Labour accused her of running out of ideas.
The scale of the opposition to the PM’s plans was laid bare today as Remain plotter MPs finally unveiled their bid to water-down and or block Brexit altogether
Tory MP Dominic Grieve and Labour’s Yvette Cooper have tabled their Brexit amendments which will be voted on in a crunch Commons showdown next Tuesday.
Ms Cooper’s amendment would suspend parliamentary rules to allow Bills tabled by backbench MPs to have priority over government business.
This would pave the way for her Bill to delay Brexit by extending Article 50 by another nine months to be debated.
While Mr Grieve has tabled an amendment which would suspend the same standing order to let MPs take control of debates and hold indicative votes on Brexit.
Remainer MPs will use the tactic to push for a softer Norway-style agreement, block a no deal and even call for a second referendum.
Although Tory MP and Brexiteer Andrew Murrison has retabled his amendment which would insert an end date to the Irish backstop.
Some believe that if MPs pass an amendment which backs an end date to the backstop then it will pile pressure on Brussels to fundamentally reform their deal.
Meanwhile, Remainer minister Amber Rudd has reportedly warned No10 that 40 ministers could quit if they are not allowed a free vote on extending Article 50.
But there are signs that Tory Brexiteers who deserted the PM in last week’s crunch Brexit vote could be softening their stance amidfears they could see Brexit slip away altogteher.
A series of amendment have been tabled ahead of the next round of showdown votes in the Commons as Parliament wrestles with the Government for control of Brexit
While Jeremy Hunt warned Cabinet today the only hope of securing changes to the Irish backstop was to get a Commons vote endorsing a time limit.
The Foreign Secretary said it was the only way of persuading Brussels it finally had to give ground on the most controversial part of the divorce deal.
The current deal – vetoed by MPs last week – says if there is no permanent trade deal by the end of the transition, the UK must stay bound to the customs union while Northern Ireland would also follow some single market rules until talks conclude.
It is intended to guarantee the border between Northern Ireland and the Republic stays open in all circumstances but Brexiteers fear it would be the permanent solution.