Senior Labour and Conservative MPs are to ramp up efforts to block any possibility of a no-deal Brexit ahead of the vote on Theresa May’s deal, with a plan to mandate the prime minister to extend or cancel article 50 if the prospect of crashing out looms.

Efforts were kickstarted on Thursday by a cross-party group of prominent MPs led by Yvette Cooper, who tabled a new amendment to the finance bill that would only allow a no-deal exit if MPs voted to proceed with one.

Cooper, the chair of the home affairs select committee, said the risks to the UK’s economy and security were “far too high and it would be irresponsible to allow it to happen”.

The MP said she believed there was no majority in parliament for a no-deal Brexit. “But if the government won’t rule it out, then parliament needs to find opportunities to stop the country reaching the cliff edge by accident – starting with the finance bill in the first week back, then looking at every other legislative opportunity too,” she said.

The amendment has been signed by a number of influential Labour and Tory MPs and is expected to be voted on when the House of Commons returns from the Christmas recess.

MPs who have signed include Nicky Morgan, the Conservative chair of the Treasury committee, Labour’s Hilary Benn, who chairs the Brexit committee, Rachel Reeves, the Labour chair of the business committee, the Tory former ministers Oliver Letwin and Nick Boles, and the former Labour deputy leader Harriet Harman.

The effect of the amendment would be to halt one clause in the finance bill, designed to give the government the power to keep tax law working in the event of a no-deal Brexit.

If it were passed, it would mean that clause would only be allowed to come into force if there were either a Brexit deal, a decision to extend article 50, or a vote in the Commons specifically approving a no-deal Brexit.

Should the amendment fail, other bills that could be targeted with amendments include immigration, fisheries and trade.

There remains a degree of scepticism, however, as to whether no-deal amendments to those bills would be ruled within the scope of the bill and the decision would ultimately lie with the Commons Speaker, John Bercow.

Multiple cabinet ministers have privately and publicly briefed their preferred alternative routes if the prime minister’s deal fails to pass,including a second referendum and a “managed no-deal”.

The work and pensions secretary, Amber Rudd, suggested there was a “plausible argument” for a second referendum if parliament could not reach agreement on a deal. Other ministers – including the foreign secretary, Jeremy Hunt, and the international development secretary, Penny Mordaunt – have suggested the UK could mitigate the effects of no-deal, with Mordaunt suggesting a “managed glidepath” including a two-year transition to trading on World Trade Organization terms.

The justice secretary, David Gauke, is understood to have argued that a managed no-deal is “not a viable option”, telling the cabinet on Tuesday: “The responsibility of cabinet ministers is not to propagate unicorns but to slay them.”

However, on Thursday the Commons leader, Andrea Leadsom, said a managed no-deal Brexit was possible, and suggested she had been looking at the option as an “alternative solution” to the deal on offer.

In coded criticism of Rudd, Leadsom said: “We won’t have a second referendum. That is not government policy.”

May insisted on Thursday that all her ministers were “very clear … what government policy is.”

At a press conference in Lancaster House alongside the Polish prime minister Mateusz Morawiecki, May said: “Cabinet ministers and I have all been very clear that we are focusing on working on ensuring that we can get the deal that we’ve agreed with the European Union agreed and through parliament in the meaningful vote.”

She repeated that the UK was “seeking greater political and legal assurances” on the Northern Ireland backstop.

“Everybody is very clear not only what government policy is, but what we are all individually and collectively focused on is working to ensure that that deal is able to be agreed by and go through a meaningful vote in the House of Commons,” May said.

At the press conference, May said the way to avoid no-deal was to persuade MPs to vote for her deal, but she reiterated that EU citizens would have their rights protected in any event.

Brussels has said that will not necessarily be reciprocated for UK citizens in EU countries, who may not get long-term guarantees that they can remain there.

“I’ve been clear, EU citizens here would have their rights protected in a no-deal scenario,” May said, adding that the Morawiecki had offered a reciprocal guarantee.