"Productive cabinet meeting this morning - looking ahead to a busy week", May said on Twitter, as the resignations of Johnson and Davis sent shockwaves through Westminster and fuelled speculation that the turmoil could eventually topple her. Her spokesman said the cabinet had discussed the publication of a "white paper" policy document on Britain's future ties with the European Union and stepping up preparations for any no-deal outcome to the negotiations with Brussels.
This means that if there was a leadership challenge or another snap election, the Conservatives could lose their hold on Downing Street.
He also told the tabloid that he had shared advice with May during Britain's negotiations with the European Union, but said May ignored his advice.
"In a resignation letter, Davis said the "'common rule book' policy hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
"The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one", Davis said in his resignation letter to May. "He obviously likes me, and says very good things about me", he said.
Brexiteer ministers are this afternoon, I'm told, still trying to get "edits" to the final White Paper, the souped-up version of the Chequers plan.
Brexit-backing MPs, including leading eurosceptic Conservative Jacob Rees-Mogg, will also seek to force her hand by submitting amendments to a trade bill being debated in the House of Commons next week.
"Stunned that this was all one of the main architects of Brexit had to offer, all I could say was 'you know what Boris, I'd noticed".
Former Conservative party leader Iain Duncan Smith said he had "deep misgivings" about the white paper; veteran Brexit hardliner Bill Cash declared himself "deeply anxious;" and Andrew Bridgen, who has already sent a letter expressing no confidence in May to party authorities, said he "and many colleagues" had "grave concerns" about the path the government is now on, Politico reported.
She said: "Many of the intentions are reassuring". "I have a lot of respect for Boris". Maybe we'll speak to him when I get over there.
The Kremlin said it hoped for an improvement in ties following the departure of Johnson, who had angered Moscow with his vociferous accusations over the poisoning with a nerve agent of a Russian spy on English soil in March.
Sources close to Mr Trump have told The Telegraph that he is a supporter of a hard Brexit and could publicly voice support for a clean break with Brussels in a move that would pile pressure on the Prime Minister.
It was "a positive thing for the UK" if Mr Trump had a good relationship with Mr Johnson, whose successor Jeremy Hunt was looking forward to building equally good relations with his United States counterparts, the spokesman said.
Another minister from the Brexit department, Suella Braverman, was also reported by local media to have resigned. Still, this is likely to hurt the Conservative Party, as a strong majority of its voters backed Brexit in the Referendum of 2016 and are likely to feel betrayed over the very existence of Britain as a sovereign nation.
Senior Tory backbencher Sir Bernard Jenkin said: "These four amendments reflect existing Government policy, and we hope they will be welcomed by the Government".
Amid warnings from businesses that continued uncertainty is risking investment and jobs, and fears time is running out, her cabinet finally agreed on a plan last week.
Trump warned that May's proposal, which maintains much of the UK's existing trade relationship with the European Union, would kill chances of a UK-US trade deal.