MPs will attempt to force the government to return with an alternative to Theresa May’s Brexit deal within three days of her plan being defeated in parliament.

Another five-day debate leading up to a vote on May’s deal on 15 January will start on Wednesday, opened by the Brexit secretary, Stephen Barclay.

Before that, MPs must approve a business motion to allow the debate and vote to go ahead, which a cross-party group of MPs, led by the Conservative Dominic Grieve, hope to amend if the Speaker allows it.

The amendment says that following defeat of the government’s plan, which is widely anticipated, “a minister of the crown shall table within three sitting days a motion … considering the process of exiting the European Union under article 50”.

Other MPs who have signed the amendment include the former Tory cabinet minister Sir Oliver Letwin and ex-Tory ministers Jo Johnson, Guto Bebb and Sam Gyimah. It has also been backed by Labour MPs including Stephen Doughty and Chris Leslie.

Sarah Wollaston, the Conservative chair of the health select committee, who also signed the amendment, said the aim was to prevent the government “running down the clock” towards no deal. Previously, the Commons had mandated the government to make a statement within 21 days.

“If and when the PM’s plan is voted down on Tuesday, MPs can’t be made to wait potentially until 12 Feb for the next vote. The situation is too urgent now,” Leslie said.

A previous amendment by Grieve that the Commons voted through before Christmas means that any statement the government brings forward after a defeat is in itself amendable – allowing MPs to put forward their own alternatives for the future of the Brexit process.

The government’s business motion has been tightly drafted, meaning the amendment may not be selected for a vote because the terms of the motion suggest that only a government amendment is permissable.

Galvanising MPs

The move comes after the government suffered a significant defeat on the finance bill, in which a powerful cross-party group of MPs led by Labour’s Yvette Cooper passed an amendment limiting the government’s tax administration powers in the event of no deal, unless no deal was explicitly endorsed by MPs.

Those behind the amendment’s success conceded it may have little material effect on no-deal preparations. Instead, its purpose had been to galvanise MPs across the House of Commons and proves there was a parliamentary majority to oppose no deal.

The rebels said they could seek to amend any and every piece of legislation the government brings to parliament between now and March.

At the cabinet meeting on Tuesday, May conceded to senior ministers she was on course to lose next week’s vote and told her cabinet she would respond swiftly with a statement to the House of Commons.

The prime minister is still seeking a form of legally binding reassurance from the European Union about the temporary nature of the backstop in the withdrawal agreement, the main bone of contention that has led Tory MPs to reject her deal.

David Lidington, May’s de facto deputy, said on Wednesday MPs should not expect Brussels to unpick the withdrawal agreement. “I don’t think that the British public are served by fantasies about magical alternative deals that are somehow going to sort of spring out of a cupboard in Brussels,” he told BBC Radio 4’s Today programme.

“This deal on the table has involved some very difficult give and take on both sides and if you go around and talk to the other EU 27 governments they will say that there are elements of this that cause them some political pain, but they are very clear, in conversations I have had with them as well as their public statements, they ain’t going to be going back and unpicking this for some brand new brilliant renegotiations.

“So, the choice that people have is this deal or it is no deal or it is, as some MPs advocate, to reverse the 2016 referendum entirely.”

By Jessica Elgot, Political correspondent