Theresa May has just 48 hours to persuade Remainer cabinet ministers against backing plans for parliament to seize control of Brexit and delay Britain’s departure from the EU.

The prime minister will make a statement urging members of her own front bench not to support the proposal on Wednesday, despite also revealing that the historic vote on her new Brexit deal is now likely to be just 17 days before the UK is set to depart.

Pro-EU cabinet ministers who previously threatened to back delaying Brexit have indicated they will “listen carefully” to Ms May, but the chances of the prime minister suffering a damaging defeat over it this week look high.

MPs are guaranteed a chance to vote on the cross-party proposal to stop a no-deal scenario on Brexit Day, 29 March, after Ms May revealed on Sunday she would not be able to put a new withdrawal agreement in front of the Commons this week and instead would delay it to Tuesday 12 March.

Despite a series of meetings between her officials, top European Commission figures and EU nation state leaders, Ms May said she still needs more time to secure necessary changes to the existing withdrawal agreement.

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Pensions secretary Amber Rudd, justice secretary David Gauke and business secretary Greg Clark have all said they are ready to back the plan to stop no deal, while others in cabinet and at more junior ministerial levels have indicated they could resign if Ms May does not take no deal off the table.

But after Ms May indicated she would make a last-ditch bid to dissuade them, one source close to the Remain wing of the cabinet told The Independent: “The clock is ticking and no deal is unacceptable, so we’ll listen carefully to what the PM has to say on Tuesday.”

Due to previous Commons votes, Ms May promised that if she had not secured a new deal with the EU by this Wednesday she would place an “amendable motion” before MPs.

This is a mechanism by which other members of parliament can bring forward their own proposals for next steps in the Brexit process – by adding amendments to the prime minister’s motion.

There is strong backing from within Ms May’s ministerial team for the plan put forward by senior Labour backbencher Yvette Cooper and ex-Tory minister Oliver Letwin, allowing MPs to seize control of the parliamentary calendar so as to pass legislation delaying Brexit if the prime minister’s agreement fails to pass.

Theresa May is recklessly running down the clock in a desperate attempt to force MPs to choose between her deal and no deal. Parliament cannot stand by and allow this to happen Shadow Brexit secretary Sir Keir Starmer

As Ms May announced she would not be able to put a new deal to the Commons, she said she would ensure that it does happen by 12 March at the latest, and went on to signal that she would make an attempt to avert the frontbench rebellion on Wednesday, saying: “We don’t know what amendments are going to be tabled.

“We don’t know what amendments are going to be selected. You haven’t even seen what motion the government is going to put down – as I say, it won’t be the meaningful vote.

“I will be making a statement to parliament on Tuesday. And then, obviously, we’ll be having the debate the next day.”

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One option open to her could be to offer ministers and MPs who are worried about a no-deal Brexit another way to stop it from happening instead of backing the Cooper/Letwin amendment.

But while the prime minister has already managed to push back attempts by MPs to back the proposal, Brexit day is now so close that many of those minded to support it believe this could be their last chance.

The prime minister’s promise to bring her new deal before the Commons by 12 March is also significant, because if the Cooper/Letwin plan is passed on Wednesday it would require MPs to vote on the actual legislation delaying Brexit on 13 March.

That means Ms May will have one final opportunity to get her deal through, and could also tell Tory Brexiteers that the UK’s departure would be delayed if they still refuse to back her withdrawal agreement on that day.

The PM’s move to delay bringing any new deal before the house was attacked by critics in the UK and on the continent. Ms Cooper branded Ms May’s actions “utterly shambolic and irresponsible”.

The Labour MP added: “She cannot just keep drifting and dithering like this or there is a real risk our whole country tumbles off a cliff edge into a chaotic no deal that no one is ready for and that would hit food prices, medicine supplies, manufacturing and security.”

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Shadow Brexit secretary Sir Keir Starmer called Ms May’s decision over the timing of the meaningful vote “an admission of failure”, adding that it represents “the height of irresponsibility”.

He went on: “Theresa May is recklessly running down the clock in a desperate attempt to force MPs to choose between her deal and no deal. Parliament cannot stand by and allow this to happen.”

Ms May met European Council president Donald Tusk for talks on Sunday afternoon, and was set to hold a number of meetings with European leaders on the fringes of the summit she is attending in Egypt.

But at least one senior European figure was unhappy with her decision to delay the vote. The European parliament’s Brexit spokesman Guy Verhofstadt said on Twitter that he had “seen many surprising decisions in a lifetime in politics. But this is close to being one of the most reckless.”

There were even uncorroborated reports that EU officials were looking at delaying Brexit to 2021 to allow time to fully plan an orderly withdrawal.

Josh Hardie, CBI deputy director-general, said of Ms May’s announcement: “This is the latest signal to businesses that no deal is hurtling closer.