British PM May warns: Back me or risk 'no Brexit at all'

Davis, writing in the Sunday Times, said it was an "astonishingly dishonest claim" to say there is no worked-out alternative to May's plan. He said her plan would allow EU regulations to harm British manufacturers.

"Be in no doubt: under the government's proposal our fingers would still be caught in this mangle and the EU would use it ruthlessly to punish us for leaving and handicap our future competitiveness," Davis said.

Steve Baker, a senior lawmaker who served as a deputy to Davis in the Brexit ministry before resigning with his boss, said May had presided over a "cloak and dagger" plot to undermine Brexit.

May's position was further undermined by Trump who said in an interview published in Rupert Murdoch's Sun newspaper on Friday that her proposals would probably kill off any chance of a post-Brexit trade deal with the world's biggest economy.

May on Sunday revealed that Trump had previously advised her to sue the EU rather than enter into an exit negotiation with the bloc.

"He told me I should sue the EU," she told BBC television. "Sue the EU. Not go into negotiations - sue them."

Though Trump later contradicted his comments by then promising a great U.S. trade deal, the president made clear his admiration for the 54-year-old Johnson, who Trump said would one day make a great British prime minister.

Steve Bannon, Trump's former adviser, was even quoted by Britain's Daily Telegraph as saying that it was now time for Johnson to challenge May for her job.

"Now is the moment," The Telegraph quoted Bannon, Trump’s former strategist and a key player in his 2016 election campaign, as saying.

"If Boris Johnson looks at this... There comes an inflection point, the Chequers deal was an inflection point, we will have to see what happens," Bannon said.

Johnson, the face of the Brexit campaign for many has remained silent in public since he warned in his resignation letter on July 9 that the "Brexit dream" was being suffocated by needless self-doubt.

When asked on Sunday if she would stand if a Conservative Party leadership contest was triggered, May declined to directly answer saying: "I am in this for the long term."

The extent of the danger to May from rebels in her party will become clearer over the course of two debates in parliament this week.

Pro-Brexit lawmakers are expected to use a debate on Monday on customs legislation to try to force her to harden up her Brexit plan, while a debate on trade on Tuesday will see pro-EU lawmakers push for even closer ties with the bloc.

Brexiteer rebels are unlikely to have enough support in parliament to win a vote, but the debate will show how many in May's party are prepared to vote against her at a time when some are looking to gather the numbers needed to challenge her leadership.

If May does clinch a Brexit deal with EU leaders, lawmakers could still vote it down.

Voting down a divorce deal so late in the process would trigger a major political crisis in Britain which would then be on course to crash out without any formal Brexit arrangements for trade, immigration and security.