THERESA May’s chances of a Brexit breakthrough appear to have narrowed considerably after Brussels all but rejected every one of her three proposed options.

As she prepares today for another meeting with Jean-Claude Juncker to present “new legal proposals,” the Prime Minister risked confrontation with right-wing Brexiteers after it was suggested the so-called Malthouse Compromise, which seeks to bring together MPs from the Remain and Leave wings of the party, was all but dead.

The Conservative compromise seeks to replace the backstop with a free trade agreement using modern technology to avoid customs checks on the Irish border while extending the transition period for an extra year until December 2021 to allow more time to agree a new trading relationship.

However, it was suggested Mrs May told colleagues during the weekly Cabinet meeting yesterday that there was now no chance of working up the “alternative arrangements” plan into a firm solution in the time left before Brexit Day on March 29.

This followed a meeting between Stephen Barclay, the Brexit Secretary, and Michel Barnier, the EU’s chief negotiator, when the Malthouse Compromise proposals were discussed. No 10 pointed out how Brussels had “expressed concerns about their viability to resolve the backstop”.

On Tuesday evening, the PM met with those backing the Malthouse Compromise to discuss their proposals. But afterwards Brexiteers Jacob Rees-Mogg and Steve Baker emerged to suggest the compromise plan was “alive and kicking”.

Yet it emerged that the alternative arrangements blueprint would only form part of the discussions on the future relationship not on the current withdrawal process.

Labour's Ian Murray MP, speaking on behalf of the pro-EU Best for Britain campaign, accused UK ministers of "chasing unicorns to appease hardline backbenchers".

"The EU won't grant any substantial changes to the backstop and a few wishy-washy legal statements won't please the ERG extremists," declared the Edinburgh MP.

"This nonsense is all part of the Government's game to run down the clock. Parliament must act now to remove no-deal and thereby take the Government's blackmailing weapon away."

Earlier in the day, the Commission had dismissed the two other options being worked on by UK ministers and officials: a time-limit to the backstop and a unilateral exit mechanism.

"The EU will not reopen the Withdrawal Agreement,” declared Margaritis Schinas, the European Commission spokesman. “We cannot accept a time limit to the backstop or a unilateral exit clause," he added.

Later, No 10 made clear it was still the PM’s intention to reopen the Withdrawal Agreement to get the backstop changed in a way that would win majority support in the Commons.

Asked if, during all the recent talks, Mrs May told her Cabinet colleagues progress had been made, her spokesman replied: “The Brexit Secretary said he had a constructive meeting. The PM has had very extensive engagement with foreign leaders. But obviously there is more work still to do and the PM will be continuing her discussions with Jean-Claude Juncker tomorrow.”

On Monday, four Cabinet ministers met the PM to urge her to extend the Article 50 process if by next Wednesday’s crunch Commons vote she had not achieved major concessions from the EU. They were Amber Rudd, Greg Clark, David Mundell and David Gauke, the respective Secretaries of State for Work and Pensions, Business, Scotland and Justice.

A senior Whitehall source said Mr Mundell came away from the meeting believing there was now a “good chance” that Mrs May would extend Article 50. No 10 insisted she would not and Britain would be leaving on March 29.

As Mrs May travels again to Brussels today for more talks with the European Commission President, Geoffrey Cox, the Attorney General, tasked with finding a legal solution to changing the backstop, will also be in the Belgian capital and is due to make a speech on the success or otherwise of his mission. Mr Barclay is also set to have more talks with Mr Barnier.

Ahead of his meeting with the PM this evening, Mr Juncker struck a downbeat note, saying: “There is not enough movement for me to be able to assume that it will be a productive discussion.”

It is expected in the next 48 hours that Downing St will confirm whether or not Mrs May will attend Sunday’s EU-Arab summit in the Egyptian resort of Sharm-el-Sheikh, which would provide an opportunity to talk to European counterparts as the clock ticks down rapidly to Brexit Day.

Three days later she will face MPs in the Commons vote, which one Cabinet colleague described as the “moment of truth”.