The result would give the new party almost 50 seats in the House of Commons, transforming the political landscape amid widespread public anger at the mainstream parties’ handling of Brexit.
Mr Farage’s party would receive 20 per cent of the vote, according to the ComRes survey for The Sunday Telegraph.
In a major blow to Theresa May, only 19 per cent of people polled said they would vote for the Conservatives – a result that would be the worst in the party’s history.
The Brexit Party has topped recent polls for the European parliament elections later this month, but the ComRes survey is the first to suggest it could enjoy similar success in a general election.
The finding is likely to add to pressure on the prime minister to announce a timetable for her resignation, as she faces growing calls from Conservative backbenchers to quit within weeks.
The poll suggests Labour would win a general election with 27 per cent of the vote, although such an outcome would see it fall short of the 326 seats needed to win a majority.
Jeremy Corbyn‘s party is on course to win 316 seats – meaning it would be the biggest party in the Commons by some way – while the Conservatives would get 179 and the Brexit Party 49.
A number of cabinet ministers and potential successors to Ms May would lose their seats if the poll findings proved correct. Cabinet ministers Brandon Lewis, Penny Mordaunt and Matt Hancock would see their seats taken by the Brexit Party, while prominent Eurosceptics Boris Johnson and Iain Duncan Smith would lose theirs to Labour.
Andrew Hawkins, chair of ComRes, said: “This is a disaster for the Conservative Party. Worse still, it was entirely foreseen.”
He added: “The longer Theresa May is in denial about the danger her party faces, the harder it will be to recover lost voters – and the more likely the Brexit Party will succeed in its aim of getting a foothold in Westminster.
“If the Conservative leadership contenders are not careful, there will be no party for them to lead.”
In a further blow to Ms May, a separate poll found that the Conservatives are on course to come fourth in European parliament elections on 23 May, receiving less than a third of the votes that the Brexit Party is expected to.
The Opinium survey for The Observer suggests Mr Farage’s party will win 34 per cent of votes – some way ahead of Labour on 21 per cent, the Liberal Democrats on 12 per cent and the Conservatives on 11 per cent.
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