Boris Johnson (file) in March.
A Downing Street spokesperson said: "This afternoon, the prime minister accepted the resignation of Boris Johnson as foreign secretary".
It comes as the Tory government tries to get a handle of infighting over how best to deal with Brexit.
"What we are doing is delivering on the vote of the British people. that's what our proposal does", she told reporters at a North Atlantic Treaty Organisation summit in Brussels.
They also argued that the proposals breach several of the "red lines" that the government had set out, including a commitment to leave the EU's tariff-free customs union.
Jacob Rees-Mogg told talkRADIO earlier today (July 10) that he did not know if any MPs had submitted a vote of no confidence.
But others argued May had adopted the most realistic plan after she was weakened in an ill-judged election a year ago when she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern.
"Brexit should be about opportunity and hope", Johnson said in a scathing resignation letter that was echoed in headlines in a number of Britain's national newspapers.
Davis resigned because he did not agree with a policy which effectively kept Britain so close to the EU's orbit.
When Brexit Secretary Dominic Raab stood up to present the plan in the Commons, MPs loudly complained they had not seen a copy beforehand - prompting the speaker to suspend proceedings for five minutes to allow them to obtain one.
He told the BBC that he thought the United Kingdom was giving away "too much, too easily" and predicted that the European Union would be demanding more concessions in talks.
"I think it is right that the cabinet backs the prime minister and speaks with one voice and if people don't do that then they have to go", Justice Secretary David Gauke told BBC radio.
It suggests a free trade area and "common rule book" with the European Union in goods after pressure from businesses to allow cross-border trade to continue as normal.
She paid tribute to Mr Johnson's "passion" in championing a global Britain after Brexit and Mr Davis' work in steering through key Brexit legislation.
He said: 'We are now in the ludicrous position of asserting we must accept huge amounts of precisely such European Union law, without changing an iota, because it is essential for our economic health - and when we no longer have any ability to influence these laws as they are made.
A precursor to this could be the government losing the vote it has promised parliament on the final exit deal.
He said trade agreements and some issues regarding the Ireland-Northern Ireland border need to be hammered out.
What was the reaction in the Commons?
But he said backbenchers had sympathy with Mr Davis, not because they agreed with his objections to the Chequers proposal, "but there was a feeling that he had been slowly pushed out of the process of making decisions".
Officials say the chances of no deal have risen significantly over the past three months, and warnings about that prospect have moved to the top of the agenda in meetings with business representatives, the person said. "It makes it unlikely that those leaders will pressurise Mrs May for further concessions".
What has been the reaction from the EU?
"My concern is about the policy rather than the individual", he said.
What does it all mean for Brexit?
Amendments tabled to the customs bill threaten to undermine Theresa May's plan for future UK-EU relations.
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