A study by Opinium put Labour on 33 per cent, the Conservatives on 26 per cent and the insurgent Brexit Party on 17 per cent, when the public was grilled on how they would vote in a general election.
The Liberal Democrats were on 6 per cent, with Ukip, the Green Party and the new centrist party Change UK all on 4 per cent.
In a fresh headache for Theresa May, the former Ukip leader’s new party was neck and neck with Labour on 28 per cent for next month’s European elections, while Tory support collapsed to 14 per cent in the 23 May contest.
Support for the Brexit Party ahead of the European elections has surged from 12 per cent in the past two weeks, with voters apparently flocking to it from Ukip.
The poll also found more than half the public (55 per cent) believe the UK should never have held the EU referendum as it has been so difficult to agree a deal.
Tory chair Brandon Lewis said he understood the “huge frustration” of Conservative members over Brexit, as the party faced pressure on the doorstep ahead of the local elections on 2 May.
The party is still hoping to avoid the European parliament elections at the end of May by approving a Brexit deal, however time is running out for the prime minister to bring forward the legislation to parliament.
Mr Lewis insisted it was still possible to avoid those contests having to take place, telling the BBC’s Andrew Marr Show: “I hope that between now and the European election polling day on 23 May, if we have to have those elections, over the next few weeks I hope that Conservative members, colleagues, volunteers, activists will come to want to not just vote for, but campaign for Conservatives to get elected, because ultimately Conservative representation is better than any other party.
“I fully appreciate the huge frustration that particularly our members and councillors have that we haven’t left the EU yet and we might have to fight these elections at all.
“But if we do, I hope they’ll vote Conservative.”
Tory bosses warned MPs and grassroots activists against supporting Mr Farage’s party, after MPs such as Telford’s Lucy Allan sent their encouragement to the Conservatives’ rivals.
A leaked email to activists, obtained by The Sunday Times, said: “All party members, including elected representatives at all levels, are expected to fully support the party in all elections.
“Campaigning for or endorsement of any other political party is incompatible with membership of the party ... The board will not hesitate to enforce these rules.”
Opinium Research carried out an online survey of 2,004 UK adults from 21-23 April. Results have been weighted to representative criteria.
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