A new cross-party group of MPs plans to thwart Brexit by swinging the Commons behind a second referendum as soon as Theresa May requests parliament’s backing for a deal with the EU, as pressure mounts on party leaders to put the issue back to the people.

Tory, Labour and SNP members say they will table a “killer” amendment in favour of a public vote. The amendment, if passed, will state that acceptance of the prime minister’s deal must be dependent on a public vote taking place beforehand, in which people would be offered the choice of leaving on the terms of that deal, or staying in the EU.

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The group, led by the Tory MP and former GP Sarah Wollaston, is determined to maintain the momentum from last weekend’s march through London by 700,000 people in favour of a people’s vote, by showing remainers that MPs in all the main parties are prepared to fight for them in parliament.

Wollaston is working with a team of two other GPs – the Tory MP Phillip Lee and Labour’s Paul Williams – and the SNP’s Philippa Whitford, who is a surgeon. They are particularly concerned by the effect Brexit will have on the NHS but warn it will also be a catastrophe for the economy and jobs.

They believe the move has the backing of more than 100 MPs, and that they have a chance of pushing the amendment through if the Labour leadership shifts position and whips its MPs in favour of a second vote.

A senior Labour figure who backs the move said: “There are some supporters of a second referendum who think the main push should come later, amid the chaos that would ensue from May’s deal failing to get through parliament or a no-deal. But we believe a killer amendment like this could be our only chance. We cannot afford to miss it.”

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The prospect of such a vote will increase the pressure on the Labour leader, Jeremy Corbyn, who would prefer a general election to a second vote. A majority of his party members and activists want a second referendum, and most would prefer to stay in the EU rather than accept a poor Brexit deal.

Wollaston, who spoke at the “people’s vote” march, said: “Without a second referendum vote on the final deal there is no informed consent to Brexit. The consequences will last for generations. Valid consent requires the government to set out the final version of Brexit and allow people to weigh up the risks and benefits.

“Quite simply Brexit will be bad for health, science and the economy in ways that will touch all our lives. As a group of four current and former clinicians we feel that the principle of informed consent is as important when it comes to Brexit as it is to patients when weighing up the pros and cons of surgery.

“People must have the right to look at the final plans, the evidence about consequences and have the opportunity to change their minds.”

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Williams said: “Before politicians make the biggest leap that this country will make in all of our lifetimes, we should check with people to make sure this is really, really what they want to do. We now know so much more than we did in 2016. Companies are stopping investments in the UK. NHS staff are leaving because they don’t feel welcome. Medical research collaboration with Europe is ending.

“Our country will become poorer, have less influence and have less control with the type of Brexit deal that Theresa May is agreeing. Is this really a price worth paying?”

Senior ministers confronted the prime minister last week over their suspicions that No 10 will agree a deal that they could never accept. At a stormy cabinet meeting on Tuesday, May was told there must now be the “closest possible political supervision” of the Brexit negotiations.

Ministers demanded a full cabinet discussion, including an assessment by the chief whip, Julian Smith, and a legal ruling by attorney general, Geoffrey Cox, before Britain signs anything. The so-called “Irish backstop”, demanded by the EU and agreed to by May last year, would at the very least keep Northern Ireland tied into the EU’s customs and standards rules.

Ireland’s EU commissioner, Phil Hogan, told May there was no chance the EU would back down on the issue. “Nobody should be in any doubt about the unity of the EU to ensure that the commitment to an operational backstop on the island of Ireland is honoured and included in the withdrawal agreement so that a hard border on the island of Ireland is avoided,” he told the Observer.

In a hair-raising rundown of planning for a no-deal Brexit, Dominic Raab, the Brexit secretary, told colleagues he was looking at whether trade could be rerouted through Dutch and Belgian ports should the French take a “tough stance”. He said Britain was highly dependent on the Channel tunnel and said the private sector should “think creatively” to help solve the capacity problem at UK ports.

On aviation, it was pointed out that while companies such as Ryanair could move their headquarters to keep planes flying between EU destinations, this was “not an option for British Airways”. It was also announced that the government was about to tender for warehouse space to store crucial medicines.

Leaders of the SNP, the Greens, Plaid Cymru and the Liberal Democrats met the EU’s chief negotiator, Michel Barnier, in Brussels last week. In an article written after the talks, Liz Saville Roberts, Plaid’s leader at Westminster, and the Lib Dem leader, Vince Cable, said one message had been that Labour was now the main obstacle to another referendum.

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At its party conference earlier this month Labour said it would push for a general election in the event of Brexit chaos, but another referendum was an option if it could not force one.