Barely half of Theresa May’s own councillors plan to vote Conservative at the European elections amid growing signs of an exodus to Nigel Farage’s Brexit Party, a poll has found.

The Survation survey for the Mail On Sunday found just 52 per cent of Tory councillors, who should in theory be among the Prime Minister’s most loyal troops, intended to stick with her.

Two-fifths said they would rather vote for Mr Farage’s new party because of her mishandling of Brexit and its potential delay to October 31.

Three-quarters said she should resign (42% now and 33% after a Brexit deal), and 96% said the Brexit impasse on her watch had damaged the party.

Boris Johnson was the most popular candidate to replace her, although almost as many councillors said they would have Mr Farage as their leader if they could.

Given a free choice, 19% would back the former foreign secretary and 15% Mr Farage.

The survey also found Mr Johnson could stem the collapse in support, with 65% ready to vote Tory if he were leader, with only 22% said they would still vote for the Brexit Party.

One of the 781 councillors surveyed last week said: “The Conservative Party is dead. It will take a strong leader to dredge it out of the mud.” Another said: “For God’s sake get on with it [Brexit]. It is killing us on the doorstep.”

A separate survey for the influential ConservativeHome website also found 62% of ordinary Tory members would vote for the Brexit Party, compared to just 23% supporting their own party.

The website called the result “the most astonishing we have ever published”.

The Sunday Times also reported that when Tory MPs return to Westminster this week, after hearing the rage in their local associations, they will mount a fresh attempt to topple the PM. Under current rules, she is protected until December because she survived a vote of no-confidence before Christmas.

Read more: Members 'won't mention Theresa May on doorsteps' as Tories prepare for election drubbing

Tory MPs are now pressing the 1922 Committee, which represents backbenchers, to change the rules to allow another such vote far sooner.

The paper reported that Sir Graham Brady, the committee’s chairman, is ready to tell Mrs May 70% of her MPs want her to resign, and that unless she agrees to go by June 30, the rules would be changed to force her out.

Separately, a petition by local Tory association chairman and women is set to pass the 65-signature threshold to call an emergency summit of the party’s senior activists to get rid of her.

The Brexit delay means the UK must participate in the European election on May 23 unless MPs can, improbably, agree on a compromise deal first.

The surge in support for Mr Farage’s party, which is predicted to win the election despite launching only this month, has also exacerbated internal problems for Labour.

Deputy leader Tom Watson said yesterday that the party would hand victory to Mr Farage if it continued to “sit on the fence” and offer “mealy-mouthed” support for a People’s Vote.

Writing in the Observer, he said the party must unambiguously campaign for a second EU referendum. He said a confirmatory referendum on any deal was “the very least” voters should expect, and should not be the grudging extent of Labour’s position.

Read more: Ian Duncan Smith tells Theresa May to quit as European rout looms

He wrote: “Labour won’t defeat Farage by being mealy-mouthed and sounding as if we half agree with him. We won’t beat him unless we can inspire the millions crying out for a different direction. We won’t win if we sit on the fence about the most crucial issue that has faced our country for a generation.”

He said both Leavers and Remainers deserved “a Labour Party that offers clarity on this issue, as well as the radical vision for a new political economy achieved by working with our socialist allies inside the EU.

“And, above all, they deserve better than Nigel Farage’s promise of a far-right Brexit that would solve nothing.”

But in a sign of the stark division at the top of Labour on the issue, Mr Corbyn told the Sunday Mirror he was not worried by Mr Farage, dismissing his platform as “simple populism”.

He said: “Farage just says, Let’s get out of Europe without a deal. But I do think he has to be challenged. If you just walk away from Europe, the complications are immense. There’s a very integrated manufacturing process with us and Europe.

“Many of our factories rely on just-in-time deliveries from Europe and deliver to Europe on a just-in-time basis. If that is disrupted there are massive problems.”

Mr Farage accused Mr Watson of breaking his promise to the people, claiming a second referendum would be “a total insult” to  five million Labour Leave voters.

He added: “I intend to wholeheartedly target Labour lies and dishonesty in the weeks ahead.”  

He also said many Tories were so angry about Brexit they would never vote Tory again.