When Cameron resigned after defeat in the Brexit referendum, Davis was appointed back in government by May, Cameron's replacement.
Davis quit late Sunday, saying he could not support May's plan to maintain close trade and regulatory ties with the European Union, commonly known as a "soft Brexit", after the departure takes place next year.
Conservative lawmakers also worry that leadership election so close to Brexit - due to take place on March 29, 2019 - would embolden Labour and increase pressure for another election which could delay Brexit.
Minister in the Brexit department Steve Baker has also resigned.
Davis' departure comes just nine months before Britain is scheduled to leave the European Union and 15 weeks before a final deal is to be signed.
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The prime minister hammered out a compromise with her deeply divided cabinet in an all-day meeting at Chequers on Friday, but after consulting friends and allies since, Johnson decided he could not promote the deal.
Some Brexit-supporting lawmakers are angry at the proposals, saying they will keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
May's plan would create a free trade area with the European Union for goods, to protect supply chains in areas such as manufacturing, while maintaining flexibility for Britain's dominant service sector.
The Common Rulebook is another way of saying that the United Kingdom will blindly follow European Union rules and regulations.
"I am also unpersuaded that our negotiating approach will not just lead to further demands for concessions", he said, concluding that his post required "an enthusiastic believer in your approach, and not merely a reluctant conscript".
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May has responded to Davis' resignation with a two-and-a-half page letter of her own, saying she does "not agree" with Davis' characterization of Friday's proposal, instead calling it a "precise, responsible, and credible basis" for UK-EU relations.
Tory MP Jacob Rees-Mogg said a "large number" of his colleagues would vote against the plan which he told LBC Radio "would not deliver Brexit".
"A wider rebellion, a leadership challenge, early elections and possibly another major shift in the Brexit strategy (either way) can not be ruled out", Citi said in a note to clients.
Davis has been locked in bitter disputes with the Prime Minister and her chief Brexit adviser Olly Robbins for months.
Johnson has not commented publicly since Friday.
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She stamped her authority on her government and told ministers to back the plan for close ties to the bloc or leave. Michael Gove, May's environment minister, said on Sunday that while the agreed negotiating stance was not ideal, he believed it delivered on handing back control to Britain.