It was reported that the former prime minister David Cameron had been drafted in before the meeting to urge him not to resign.
His shock departure was followed by that of Brexit ministers Steve Baker and Suella Braverman, all co-ordinated as part of a bombshell move on Sunday night.
Conservative MP Jacob Rees-Mogg, a leader of the party's "hard Brexit" faction, compared May's plan to an egg so softly boiled that it "isn't boiled at all".
An opinion poll found that 35 per cent believe the Brexit compromise agreed by the Cabinet is the best deal Britain will get from the European Union, while 38 per cent dismissed it as a sell-out.
Ian Lavery, chairman of the main opposition Labour Party, said: "This is absolute chaos and Theresa May has no authority left".
In that meeting, May had appeared to win over her fractious cabinet and secure approval for her plan, which was to be published as soon as this week in a lengthy white paper that would stake out Britain's vision for future relations with Europe.
"He is exchanging (resignation) letters with the PM", the source said.
- Davis led Britain's negotiations in Brussels on the terms of the European Union divorce, and the future relationship with the bloc.
Iranian teen detained over Instagram dance videos
In one video, she spoke about the history of parkour, an outdoor activity popular in Iran , and about women practitioners. Another post showed a man holding a birthday cake and dancing, with the comment , "dancing isn't a crime".
Davis said the plan would "make the supposed control by Parliament illusory rather than real".
Hard-line Brexit backers who argue that May should have a clean, decisive break from Brussels, spent the weekend complaining that her recently revealed proposals were a timid capitulation, a "Brexit in name only", that ignored "the will of the people" who voted 52 to 48 percent in June 2016 to leave the European bloc.
"Obviously if the Government and the Prime Minister continue to support that very poor offer then I won't have any confidence in the Government or the Prime Minister".
Asked if the prime minister could survive.
Allies made it clear that the foreign secretary has not chosen to publicly support the Chequers deal yet - unlike Environment Secretary Michael Gove, Commons Leader Andrea Leadsom, and Trade Secretary Liam Fox.
Others were understood to have already handed in their letter to 1922 Committee chair Sir Graham Brady due to concerns the Government had "capitulated" when it came to her own Brexit red lines. One other ministers in his department has also quit, with reports that another has done so.
He became the public face of Brexit, leading the British delegation in talks with Brussels, although his role had been increasingly overshadowed in recent months as May and her aides took a bigger role in the negotiating strategy.
Peter Bone, a Eurosceptic MP allied to Mr Davis, told the BBC that he didn't see how the prime minister could get her Brexit plans through Parliament, and also that he couldn't see how she continue in her position if she didn't give into anger from the Conservative backbenches.