Brexit-backing members of Ms May’s team will meet within days to discuss their approach, with a drive to change the text of the UK’s withdrawal agreement not ruled out.
It emerged as Ms May sought to shore up her leadership following a wave of resignations, by appointing staunch ally Amber Rudd back to the cabinet six months after she was forced to resign over the Windrush scandal.
Downing Street is on high alert as rebel backbenchers submitted further letters calling on Ms May to quit, ahead of a possible vote of no confidence next week.
The Independent understands that House of Commons leader Andrea Leadsom is set to convene the meeting of Brexiteer frontbenchers to decide how Ms May’s strategy might evolve ahead of a critical European summit in just over a week.
As it emerged he would continue in post, the environment secretary said: “I think it’s absolutely vital that we focus on getting the right deal in the future.”
They will look at how they can allay deep concerns within the party about the backstop mechanism, which binds the UK into a customs union with the EU if no trade deal has been reached by the end of the Brexit transition period in December 2020.
Many Conservative MPs wanted the UK to have a unilateral option to withdraw from the arrangement, something Ms May had concluded is unobtainable.
One cabinet source explained that several members of the group do still want changes to the text of the withdrawal agreement, and believe it may become easier to convince the PM of their case as the prospect of defeat in the commons looms.
But the source explained that they are also realistic about the chances of success. Another insider told The Independent others were more focussed on achieving a stronger settlement in the “future framework” – outlining the UK’s final post-Brexit trading relations with the EU – which is still to be hammered out ahead the special EU summit on 25 November.
The prime minister’s spokesman said on Friday that the focus of negotiations will now be on the future trading arrangement and not the withdrawal agreement that includes the backstop. But he added: “Nothing is agreed, until everything is agreed.”
The EU have been less equivocal, with German chancellor Angela Merkel saying there is “no question” of reopening talks as a document is now “on the table”.
Ms Rudd’s return to the cabinet is a boost for Ms May, given that she has backed the current form of the prime minister’s withdrawal agreement.
After her new job as work and pensions secretary was announced, Ms Rudd told Emma Barnett on BBC Radio 5 Live: “It is quite exciting this proposal, and I certainly hope the cabinet back it.
“I think it’s the right combination. It’s a compromise. Everybody knew it was going to have be a compromise, and the people who are throwing mud at it from either side are looking for something perfect.
“Perfect was never going to be on offer.”
Earlier in the day Eurosceptic MP Steve Baker sought to pressure cabinet members by warning that any who backed Ms May’s approach could forget about becoming party leader – with Mr Gove, Ms Mordaunt, Mr Hunt and Mr Javid believed to harbour ambitions.
But a push from Mr Baker and other members of the European Research Group (ERG) of backbenches to secure a vote of no confidence in the prime minister appeared to have some way to go, with the MP making differing statements during the day on how many letters had been submitted – 48 are needed from MPs to trigger a vote.
Tory whips held a meeting on Friday ahead of a potential challenge, while Ms May conducted a conference call with Tory association chairs as she tried to build support for her Brexit deal.
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.