Rebel Tory MPs who want to keep the UK in the EU customs union and single market appeared on Saturday to be backing away from defeating Theresa May in crucial parliamentary votes this week – because they fear the resulting humiliation could threaten her leadership and let in Boris Johnson.

Before a momentous week in the Commons, several votes – including on the customs union and the role of parliament in the Brexit “endgame” – remain on a knife edge. Labour, the SNP and Liberal Democrats need only a dozen or so Tories to join them to inflict humiliation on May, and throw her Brexit strategy into chaos.

But on Saturday there were signs that May and her whips had reduced the threat level from critical to severe, as key Tory rebels said they feared that striking now could trigger a full-blown leadership crisis that would destabilise the entire party and pave the way for a hardline Brexiter such as Johnson to mount a challenge.

One former minister and leading rebel among the 12 hardliners who back staying in the customs union and single market told the Observer: “It is a political calculation. If we were to defeat her on that now, does that further weaken her and give the European Research Group [led by Jacob Rees-Mogg] more opportunities to stick their knife into her? That is not where we want to be.”

Foreign secretary Boris Johnson warned Brexit negotiations are heading for a ‘meltdown’. Photograph: Will Oliver/EPA

While some Tory rebels, including Anna Soubry and Kenneth Clarke, are among those who are still likely to vote against their own party on the customs union and other amendments, others, including former education secretary Nicky Morgan, are understood to have doubts that this week is the time to strike.

While they are still determined to secure changes to ensure Britain stays in the customs union and close to the single market, they now believe the time to do so is later in the summer when the trade and customs bills return to the Commons. May also appears to have won important support from her former home secretary, the ardent Remainer Amber Rudd, who is expected to call on Tory MPs in a newspaper article on Sunday to back the prime minister and give her support before a vital EU summit later this month.

Tensions over Brexit reached new heights last week ahead of the Commons showdowns. First, the Brexit secretary, David Davis, threatened to resign over government plans for post-Brexit customs arrangements that he saw as paving the way for long-term involvement in the EU economic model. Then it was revealed that Johnson, the foreign secretary, had been secretly taped telling Tory donors that Brexit negotiations were heading for “meltdown” and that US President Donald Trump would have handled them better.

Tory Remainers say they have been reassured that May is now moving towards a softer form of Brexit, including the possibility of a long-term customs arrangement with the EU to solve the problem of Northern Ireland.

They fear any change at the top could let in a hard Brexiter as new leader, probably Johnson or the environment secretary Michael Gove, who would prefer the hardest exit or no deal at all to secure a clean break from Brussels.

Labour leader Jeremy Corbyn is facing a rebellion by his own Remain-inclined MPs. Photograph: Wiktor Szymanowicz/Rex/Shutterstock

While May is heading for a tense two days of votes on Tuesday and Wednesday, Jeremy Corbyn is also facing a rebellion by his own Remain-inclined MPs, after they were ordered by party whips to abstain in a vote on staying in the European Economic Area (EEA) – a move that would allow the UK to stay in the single market. Several dozen Labour MPs, including several senior figures, are expected to defy the party whip and support the Lords amendment.

Hilary Benn, Labour chair of the Brexit select committee, is among them. He told the Observer: “We should keep our options open and that’s what the EEA amendment does. It would solve the Northern Ireland problem, keep goods flowing freely, ensure common standards, protect employment and environmental rights, and enable us to continue to co-operate in important areas like aviation, consumer safety and medicines. And it’s an option that the Brexit select committee has said could be an alternative.”

Labour is also being warned that the cost to the economy of its current policy – of staying in the customs union but not single market – would be £29bn by 2030, according to a study by Cambridge Econometrics. It also suggests that such a Brexit would cost 300,000 jobs, compared to staying in both.

The Open Britain campaign group says the analysis implies there would be a £1.1bn loss to the north-east economy, a £3bn hit to the north-west and a £6.3bn reduction in London. Labour currently refuses to back EEA membership for a number of reasons, including that it would mean obeying EU freedom of movement rules and would not allow membership of the customs union, therefore preventing a solution to the Northern Ireland border issue.

Meanwhile, pro-Brexit Tories are preparing to turn up the heat on May over coming weeks, demanding a major change of course amid cabinet concerns that her current strategy will end in electoral “disaster” for the party.

There is now widespread frustration among Brexiters, who believe the Brexit they sought is disappearing from view. They have now drawn up plans to “rescue the process” once the withdrawal bill passes it last major hurdle this week. Major changes in strategy are being demanded by both Davis and Johnson.

One ally of the foreign secretary said: “From the very start, Theresa and Philip Hammond have treated this as making the best of a bad job. On the Brexit side, the key is getting the withdrawal bill through with as few concessions as possible. Once you’ve guaranteed you’re leaving, even if not on the best terms, at least we’re leaving. There is then a thinking that there is time to rescue the process.

“A change at the top is one of the options. Once the withdrawal bill goes through, that will leave her more vulnerable. My instinct is there won’t be any challenge this side of March next year. But if something happens, that could quickly change.”