Reports said Mr Davis resigned on Sunday, 48 hours after Ms May announced her divided Government had at last agreed on a plan for ties with the European Union after the United Kingdom leaves next year.
Prime Minister Theresa May's government was thrown into turmoil late Sunday with the surprise resignation of David Davis, her "Brexit minister" in charge of negotiating Britain's exit from the European Union.
He also said "the general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one".
The resignation was swiftly followed by that of Steve Baker and Suella Braverman, who are not members of the Cabinet but were the Brexit Department's other elected Brexit supporters.
Brexiteer MP Jacob Rees-Mogg said it would be "very difficult" for Mrs May's plans to win the backing of MPs without Mr Davis.
BBC political editor Laura Kuenssberg said she understands Mr Davis was "furious" after a meeting at Number 10 earlier on Sunday and "concluded he could not stay in post".
"I am also unpersuaded that our negotiating approach will not just lead to further demands for concessions".
Tory MP Andrew Bridgen told the Press Association: "I can't support the offer which emerged at Chequers - I think it's a breach of the red lines, in fact the offer is so poor that I couldn't support it even if the European Union were paying us for it". She can not deliver Brexit and our country is at a complete standstill, while the Tories indulge in their leadership tussling.
"Those of us who believe that we want to execute a proper Brexit, and one that is the best deal for Britain, have an opportunity now to get behind the prime minister in order to negotiate that deal", he said.More news: OnePlus 7 might be a 5G phone released on USA carriers
"[Mr Davis'] departure raises more questions about what came out of that meeting. If the Brexit Secretary can not support them they can not be very good proposals".
It would involve a "facilitated customs arrangement" meant to remove the need for a hard border in Ireland, and the creation of a UK-EU free-trade area, in which the UK would abide by a "common rule book" of EU regulations.
It is unclear whether Brussels will accept this, after repeatedly warning Britain it can not "cherry-pick" bits of its single market.
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.
Eurosceptic MP Mr Baker played a leading role in the Brexit campaign in the run up to the 2016 referendum.
But the Prime Minister has seen a rise in support for her taking her party into the next election, due in 2022.
Noted for his love of climbing and flying, his ascent in politics began in 1987 when he was elected to parliament, representing a seat in northern England.
Mr Davis had been on the brink of resigning a few times in recent weeks, but soldiered on because he did not want to risk bringing the Prime Minister down.