The Conservative group on Derbyshire county council has taken the extraordinary step of refusing to help with the 23 May poll – insisting it “should not be happening”, because the UK should have left the EU.
The backlash over the failure to deliver Brexit comes as the prime minister faces a fresh push to change party rules to enable MPs to force her out of No 10 this summer.
The 1922 Committee of backbench MPs will meet on Tuesday to discuss removing the ban on a fresh no-confidence vote within 12 months of the last challenge – which currently prevents it from happening before December.
Meanwhile, a new poll suggested two-thirds of Conservative councillors were preparing to vote for Nigel Farage's rival Brexit Party at the European elections.
The survey of elected grassroots Tories - carried out for the Mail on Sunday - also found three-quarters of those asked wanted Mrs May to resign.
Explaining the refusal to campaign, Barry Lewis, the council leader in Derbyshire, said: “This was not an easy decision and goes against every natural instinct we have as Conservatives.
“However, we were promised, following the largest public mandate a UK government has ever received, that we would be out by 29 March.
“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.
“More significant for our residents and local businesses is the fact that the uncertainty continues.”
Mr Lewis also attacked the compromise talks with Labour, adding: “Inviting Jeremy Corbyn to the table in an attempt to pass a deal was, in our view, a serious mistake for the prime minister and, consequently, our party.
“Jeremy Corbyn and the Labour party under him, deserve no credibility.”
The election of 73 UK MEPs is almost certain to go ahead next month, the price the EU demanded for agreeing an extension to the Article 50 process until 31 October.
They will leave Brussels if the Commons ratifies the withdrawal agreement, but – with Brexiteer anger growing and the talks with Labour on the brink of collapse – that looks increasingly unlikely.
One poll suggested Mr Farage is on course for a stunning triumph, putting his party on 27 per cent of the vote, well ahead of both Labour (22 per cent) and the Tories (15 per cent).
Meanwhile, as the local elections loom, on 2 May, some Conservative activists are avoiding even mentioning the prime minister on the doorstep.
Jan French, association chair in the North East Cambridgeshire constituency represented by Stephen Barclay, the Brexit secretary, told The Daily Telegraph: “I don't talk about her at all. As far as we are concerned these are local elections and they are nothing to do with national politics.”