The Opinium poll had the party on top with 26 per cent of the vote, ahead of Labour on 22 per cent.
It is the first ever national poll to have the Brexit Party, fronted by Mr Farage, 55, on top.
The new poll has the Conservatives down in third with just 17 per cent of the vote, and the Liberal Democrats in fourth on 16 per cent.
Nigel Farage hailed the new Opinium Poll as a ‘historic’ moment as it showed his Brexit Party on top
Although the Brexit Party wouldn’t get enough seats to form a government under First Past the Post, the poll suggests that they could win the popular vote despite only being formed in January this year.
Mr Farage believes his party could be on the verge of its first seat in parliament as it contests the Peterborough by-election on June 6, and has tried to woo voters by warning if they vote Conservative, they will end up with Labour.
He has been campaigning ahead of the by-election after Labour MP Fiona Onasanya was ousted.
Mr Farage believes the election on Thursday will be a two-horse race between the Brexit Party and Labour.
In a bid to avoid splitting the vote, he has urged otherwise Tory voters to back the Brexit Party to prevent Labour from retaining their vacated seat.
Mr Farage told The Telegraph: ‘The Tory party in Peterborough are nowhere. But Labour have a massive election machine and they are throwing everything at this. And I mean everything.
Mr Farage believes his party could be on the verge of its first seat in parliament as it contests the Peterborough by-election on June 6
‘Our key message these last few days to conservative voters in the north of the constituency, is vote Conservative, get Corbyn. Only the Brexit Party can beat Labour here.’
The by-election comes in a monumental week for British politics with US President Donald Trump embarking on a state visit and Theresa May stepping down on Friday.
But Farage said he trusts none of the potential successors to Mrs May to manage a No Deal exit from the EU.
He also said his party is readying itself for a general election if the time comes and the new prime minister fails to deliver Brexit.
Mike Greene is standing in the Peterborough by-election for the Brexit Party.
Meanwhile, Donald Trump sensationally urged the British government to involve Mr Farage in Brexit negotiations with the EU.
The President hailed the Brexit Party leader as a ‘very smart person’ who could have bolstered Theresa May’s botched deal which she failed to push through Parliament.
On the eve of his state visit to the UK, his criticism of the Prime Minister’s decision to omit Mr Farage from talks with Brussels will likely put noses out of joint in Downing Street.
‘I like Nigel a lot. He has a lot to offer. He is a very smart person. They won’t bring him in,’ he told the Sunday Times.
‘Think how well they would do if they did. They just haven’t figured that out yet.’
Mr Farage struck up a friendship with Mr Trump in 2016 when he endorsed his Presidential campaign and even spoke at one of his Mississippi rallies.
Donald Trump has sensationally urged the British government to involve Nigel Farage in Brexit negotiations with the EU