No 10 is feeling the pressure to pull the plug on Brexit talks with Labour and move to an alternative plan, amid warnings that the opposition is in no hurry for a deal before the European elections.

With talks deadlocked and no sign that the government moving on its red lines, neither the Conservatives or Labour want to appear responsible for the breakdown in discussions.

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However, government sources acknowledge Theresa May is under much greater time pressure than Labour, which has little incentive to do a deal before the European and local elections that are likely to result in the Conservatives suffering heavy losses to Nigel Farage’s Brexit party.

Ministers and their opposition counterparts are taking part in working groups on some issues this week, but there will be no discussion before Easter on the big issues of a customs union or a confirmatory referendum, making it easy for Labour to reject the prime minister’s overtures so far.

The government’s alternative plan is for MPs to thrash out an acceptable version of May’s deal through a series of votes or by amending the withdrawal bill, but experts said there was barely enough time to do this in the five weeks before the European elections.

Nikki da Costa, formerly the legislative affairs director in No 10, suggested getting the withdrawal bill passed by 22 May would “require a level of legislative aggression from government not seen in this parliament”.

There is also concern in No 10 that Labour may not get behind the plan to let MPs amend the withdrawal bill to find a way forward. Downing Street is worried that if the withdrawal bill were to be voted down before the stage of amendments, May would have to prorogue parliament and start again by bringing it forward with a new session and Queen’s speech, a move also fraught with difficulties given the government’s weakened relationship with the Democratic Unionist party (DUP).

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However, Jeremy Hunt, the foreign secretary, warned on Monday that a failure to find some way of getting agreement for a deal before the European elections would be “highly, extremely, very, very challenging” for May, suggesting she may struggle to cling on longer as prime minister if that were the case.

“That would be a very serious situation – I don’t pretend otherwise – but we aren’t at that point,” he said, during a visit to Japan. Asked if fighting the elections would be a disaster for the Tories, he told the BBC: “In terms of polling, it certainly looks that way”.

He even suggested the Conservatives may have to go back into talks with the DUP, which has repeatedly rejected May’s withdrawal agreement on account of the backstop that could keep Northern Ireland in a customs union. “We don’t know if they are going to work and it may be that we need to find a way to rebuild the Conservative-DUP coalition,” Hunt said.

Other Conservatives believe the European elections are now all but inevitable, despite May’s claims that they are avoidable. One Conservative MEP told the Guardian that it was “cloud cuckoo land” to think European elections can be avoided at this stage.

Conservative party officials are privately acknowledging the party will lose around half of their MEPs. The party is so concerned about defections to the Brexit party and Change UK that all candidates are being asked to sign legal undertakings that they would resign as MEPs if they were to jump ship for another party.

“They are worried about losing MEPs on both ends of the spectrum. It could be a major embarrassment,” one candidate to become an MEP said.

A Tory party source said: “As is usual, Conservative candidates are expected to represent the Conservative party.”