However, furious pro-Brexit MPs criticised Brexiter cabinet ministers, including David Davis, Liam Fox and Andrea Leadsom, for failing to take a stronger stand against the government's proposed offer to the European Union, including quitting the cabinet. His deputy Steve Baker reportedly resigned with him.
On Friday, Davis and the rest of May's fractious Cabinet agreed on a plan for ties with the European Union after the United Kingdom leaves next year.
The Prime Minister will insist the plan, which would see the UK share a "common rulebook" for goods as part of a proposal to create a UK-EU free trade area, still meets her Brexit red lines.
His resignation seemed to spur others to follow suit, with a source saying that a junior minister in the same department had also quit, just two days after May had held a crisis meeting with ministers to overcome the deep divisions over Brexit.
While May has supported a "softer" exit from the European Union, which leaves room for trade and continued financial ties with the bloc, many conservatives prefer a total break.
Yet after reflecting on the situation, Mr Davis and Mr Baker apparently decided they could not live with such a soft Brexit after all.
FILE PHOTO - Britain's Secretary of State for Departing the EU David Davis delivers a speech on Britain's security relationship with the EU after Brexit, in London, June 6, 2018.
Tory Andrew Bridgen said he could not support the proposals that came out of Chequers, describing them as a breach of the red lines and that he wouldn't support it "even if the European Union were paying us for it".
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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.
However, in his resignation letter to the Prime Minister last night Davis wrote: "In my view the inevitable effect of the proposed policies will be to make the supposed control by Parliament illusory rather than real".
- His departure leaves May with a hard task to find a replacement who can win the confidence of the pro-Brexit faction in May's Conservative Party whilst delivering on a Brexit plan that outraged many of them.
UK Brexit Secretary David Davis has resigned, along with two other Brexit ministers.
Davis's resignation could embolden Brexit-supporting Conservative parliamentarians to challenge May's leadership.
In a September 2017 op-ed for CNN, Davis wrote: "Brexit is not about Britain stepping back from the world, but jumping into the new opportunities it presents".
Some Brexiteers dream of replacing May with a staunch Brexiteer, such as Foreign Secretary Boris Johnson, who in the past has disagreed publicly with his boss.
"The prime minister is in office but not in power".