Ministers have moved to try to head off an attempt by MPs to seize control of Commons business in a bid to secure a “softer” Brexit.
A cross-party group of pro-EU MPs claimed they had the numbers to force a series of “indicative votes” on alternatives to Theresa May’s Brexit deal.
However, Business Secretary Greg Clark said the Government was prepared to enable Parliament to express a view on the various options if Mrs May’s deal is rejected by the Commons for a third time next week.
Meanwhile, Mrs May hinted that she would not bring her beleaguered plan before MPs for another vote next week if sufficient support cannot be mustered.
In a letter to parliamentarians, she said: “If it appears that there is not sufficient support to bring the deal back next week, or the House rejects it again, we can ask for another extension before 12 April – but that will involve holding European Parliament elections.
“If it appears that there is sufficient support and the Speaker permits it, we can bring the deal back next week and if it is approved we can leave on 22 May.”
Defeat for the Government on Monday on the amendment – tabled by former ministers Sir Oliver Letwin and Dominic Grieve and Labour MP Hilary Benn – would be a further humiliation for Mrs May.
The Prime Minister was already facing a furious backlash from Tory Brexiteers after she agreed a delay to Brexit with EU leaders in Brussels despite having repeatedly promised Britain would leave on March 29.
If the amendment is passed, it would pave the way for a series of “indicative votes” in the House on Wednesday, effectively taking control of the Brexit process out of the hands of the Government.
Sir Oliver said: “We believe that we have the numbers to pass the amendment on Monday and thereby guarantee indicative votes on Wednesday.”
However Mr Clark pointed to a commitment by David Lidington, Mrs May’s de facto deputy, to “facilitate” Parliament in expressing its view if she loses the third “meaningful vote” on her deal.
“The Government will provide that so there is no reason why the Government should be forced to do something which it is committed to do anyway,” he told the BBC.
Asked if that meant Mrs May would give MPs indicative votes on the way forward, he said: “Yes.”
The prospect however infuriated Brexiteers who fear it could see the Commons pivot towards a “softer” Norway-style deal.
Steve Baker, the deputy chairman of the European Research Group, tweeted: “National humiliation is imminent through these ‘indicative votes’.”
In a further setback for the Prime Minister, the DUP – whose support will be crucial if the Government is to win the vote on her deal – indicated they would not support her.
Deputy leader Nigel Dodds said she had failed to secure any change to the Northern Ireland backstop – which the the party bitterly opposes – at the summit in Brussels.
“Nothing has changed as far as the Withdrawal Agreement is concerned. We will not accept any deal which poses a long-term risk to the constitutional and economic integrity of the United Kingdom,” he said.
Mrs May returned to London with her party in disarray and MPs openly speculating that she will be forced to quit.
Under the plan set out at the EU summit, leaders agreed to extend Brexit to May 22 if Mrs May can finally get MPs to back her deal in a third Commons “meaningful” vote.
However, if she fails the UK will have to set out an alternative way forward by April 12, which could mean a much longer delay – with the UK required to hold elections to the European Parliament – or leaving without a deal at all.
Following defeats by 230 votes in January and 149 votes last week, both pro-EU MPs and Brexiteers warned that she was heading for another heavy reverse.
Former education secretary Nicky Morgan said “there is no doubt” Conservative MPs had made clear they wanted her to go.
“If the third meaningful vote isn’t approved, I think that makes her position very difficult,” she said.
Nigel Evans, the pro-Brexit executive secretary of the backbench 1922 Committee, said “a lot of people think it is not going to be long now before she does leave Downing Street”.
Backbencher Steve Double said the next week would be a “defining moment” for her premiership and urged her to consider her position.
“I think it is quite clear that she is not leading her party. She is isolated, sadly, from a majority of the parliamentary party now,” he said.
“We need to find a way forward and I think that requires new leadership.”
However Tory grandee Ken Clarke warned that a Conservative leadership contest at such a crucial moment would be highly damaging.
“The world would finally decide that the British and their political system had gone mad if we all broke off to have six weeks of a bloody leadership campaign,” he told BBC Radio 4’s The World At One.
Earlier, aides confirmed Thursday’s agreement meant a no-deal Brexit was no longer a possibility on March 29, but stressed that it remained on the table if MPs have not approved the Withdrawal Agreement by April 12.
The format increases pressure on Leave-backing MPs to row in behind Mrs May’s deal, for fear that if it falls, the UK could find itself electing new MEPs and remaining for months or years within the EU.
Downing Street was unable to say on which day the Government would seek to bring back the Withdrawal Agreement for a third “meaningful vote” – known in Westminster as MV3.
But sources confirmed that Mrs May will table secondary legislation to remove the date March 29 from Brexit laws.