Tory councillors are revolting against Theresa May over her handling of Brexit, with 40% prepared to vote for Nigel Farage’s rival party at the European elections.

A survey of elected grassroots Conservatives found three quarters of Mrs May’s councillors wanted her to resign, with 43% of them calling for her to quit immediately.

Just over half – 52% – said they would vote Tory at the European election, a figure that would rise to 65% if Mrs May was replaced by Brexiteer Boris Johnson, the Survation poll for the Mail On Sunday found.

Some 40% said they would vote for Mr Farage’s Brexit Party, a figure that would fall to 22% if Mr Johnson was in Number 10.

There was almost complete agreement that the Brexit deadlock had damaged the Conservatives, with 96% saying the party had been harmed.

One councillor in the Survation study 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.”

Survation questioned 781 Tory councillors between April 17 and 19.

Some 43% said Mrs May should resign now and 33% once a Brexit deal has been reached – the timetable the Prime Minister has indicated for her departure.

Boris JohnsonThere was support for Boris Johnson as the next prime minister (Brian Lawless/PA)

Mr Johnson was backed by 23% as the best leader, followed by Michael Gove on 14%, Jeremy Hunt on 12%, Sajid Javid on 11% and Dominic Raab on 9%.

The Mail On Sunday report came after a survey of more than 1,000 Tory members by the influential ConservativeHome website found nearly eight out of 10 want Mrs May to quit.

And it followed the Tory group on Derbyshire County Council announcing it would not campaign for the party in the European elections.

In a sign of the pressure on Mrs May, the Sunday Times reported that she will be told within days that she must step down by the end of June or face a fresh effort by MPs to oust her.

The newspaper reported that Sir Graham Brady, chairman of the backbench 1922 Committee, will tell her that 70% of Tory MPs now want her to resign.

Mrs May survived a confidence vote by her MPs in December and the party’s rules prevent another attempt to force her out within 12 months.

But discontent with Mrs May’s leadership has fuelled speculation that those rules could be changed to allow a fresh challenge.

The ConservativeHome survey of 1,132 party members on its panel found 79% wanted Mrs May to quit and trigger a leadership contest.

The Prime Minister has said she will not lead the Tories into the next election – due in 2022 – and has promised to bring her departure forward if her Brexit deal gets through Parliament.

Former Tory MP Paul Goodman, the website’s editor, said: “It’s like Groundhog Day for the Prime Minister – but in which each one is worse than that before.

“Last month, a record total of seven out of 10 of our panel members wanted a new Party leader. This month we have a new record of nearly eight out of 10.”

Just 19% of those surveyed wanted Mrs May to stay on as leader.

Mr Goodman said: “The second postponement of Brexit and the talks with Jeremy Corbyn are undoubtedly huge contributors to this lamentable rating.

“The latter especially is making campaigning uphill work indeed for many local government candidates.

“However, we suspect the biggest factor is the European Parliamentary elections that are due to take place.”

In a suggestion that ministers should now tell Mrs May her time is up, he said: “The voluntary Party has lost confidence in the Prime Minister. Is anyone listening around the Cabinet table?”

Barry Lewis, who has led the Derbyshire authority since May 2017, said he had informed party chairman Brandon Lewis of the boycott of the European elections, which he said had received overwhelming support from his colleagues.

He said: “We were promised, following the largest public mandate a UK Government has ever received, that we would be out by March 29.

“The Prime Minister said we would be out by that date countless times, so did many others in Government, and yet here we are racing towards the end of April and facing an increased prospect of participating in a European election in May that should not be happening.”

As an extension to the Brexit process has been granted until October, the UK is obliged to elect 73 MEPs to the European Parliament who will sit until Britain leaves on October 31 or when the Withdrawal Agreement is ratified in the Commons.