Boris Johnson has launched a scathing attack on Theresa May's Brexit strategy, saying the "dream is dying, suffocated by needless self-doubt".
In his letter resigning as foreign secretary, he said the prime minister was leading the UK into a "semi-Brexit" with the "status of a colony".
His resignation came hours after Brexit Secretary David Davis quit the cabinet.
Mrs May said she was "sorry - and a little surprised" by Mr Johnson's move after his apparent support on Friday.
She said the deal agreed by the cabinet after their "productive discussions" at Chequers would "honour the result of the referendum" and allow the UK to "take back control of our borders, our law and our money".
Health Secretary Jeremy Hunt has been named as Mr Johnson's replacement as foreign secretary, with Matt Hancock as the new health secretary.
Mrs May's official spokesman said she would fight any attempt to oust her as prime minister if the required 48 Tory MPs called for a contest.
I am told 1922 committee chairman Graham Brady made it clear that the 48 signatures that would start a leadership contest hadn’t been received— iain watson (@iainjwatson) July 9, 2018
She earlier faced her critics at a packed meeting of backbench Conservative MPs, many of whom share Mr Johnson's concerns about her Brexit stance.
Loud applause could be heard at the end of the 1922 Committee meeting, which the PM attended for just over an hour.
Leaving the gathering, leading Brexiteer Jacob Rees-Mogg said he did not think there would be a confidence vote over Mrs May.
But ministerial aide Chris Green resigned his position as a parliamentary private secretary to the Department for Transport after the meeting, saying in a letter to Mrs May that she had confirmed his fears that "we would not really leave the EU" under her proposals.
Mr Johnson's parliamentary private secretary Conor Burn has also stepped down. Brexit minister Steve Baker also left the government.
Housing minister Dominic Raab has replaced Mr Davis as Brexit secretary.
What Johnson says in his resignation letter
Mr Johnson does not pull any punches, saying Brexit "should be about opportunity and hope" and a "chance to do things differently", but "that dream is dying, suffocated by needless self-doubt".
He claims crucial decisions have been postponed, including preparations for a "no-deal" scenario, "with the result that we appear to be heading for a semi-Brexit, with large parts of the economy still locked in the EU system, but with no UK control over that system".
The PM's response to Johnson
In her letter accepting his resignation, the prime minister said she had allowed cabinet ministers "considerable latitude to express their individual views" on Brexit.
"But the agreement we reached on Friday marks the point where that is no longer the case and if you are not able to provide the support we need to secure this deal in the interests of the United Kingdom, it is right that you should step down."
What prompted the row?
The UK is due to leave the European Union on 29 March 2019, but the two sides have yet to agree how trade will work between the UK and the EU afterwards.
There have been differences within the Conservatives over how far the UK should prioritise the economy by compromising on issues such as leaving the remit of the European Court of Justice and ending free movement of people.
Mrs May only has a majority in Parliament with the support of the 10 MPs from Northern Ireland's Democratic Unionist Party, so any split raises questions about whether her plan could survive a Commons vote.
She took her entire cabinet to her country residence on Friday to try to get agreement on a UK vision for post-Brexit relations.
An agreement was announced after the 12-hour meeting, but many Brexiteers have been unhappy with the deal which they think will lead to the "worst of both worlds".
Why did David Davis resign?
The man leading the UK's negotiating team, David Davis, resigned late on Sunday night, saying that he did not agree with the UK's proposals, so was the wrong person to be going into negotiations with them.
He told the BBC that he thought the UK was giving away "too much, too easily" and predicted that the EU would be demanding more concessions in talks.
Mr Davis, who had been Brexit secretary since Mrs May became prime minister in 2016, said he had made compromises since taking on the role, but this was "one compromise too far".
Theresa May is sticking by her Brexit plan
Speaking in a boisterous House of Commons, Mrs May defended the Brexit plan agreed on Friday, which would see the UK agreeing a "common rulebook" with the EU for trading in goods, but not services, after Brexit.
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.
But she told MPs: "We do not agree on the best way to deliver our shared commitments to honour the result of the referendum."
Mrs May told MPs that the plan agreed by the cabinet at Chequers was the basis of a "responsible and credible" offer to restart renegotiations with the EU.
But she warned that if the EU did not engage with her plan, there was a "serious risk" of the UK leaving in March 2019 without a deal in a "disorderly" manner.
Under her proposal, a treaty would be signed committing the UK to "continued harmonisation" with EU rules - avoiding friction at the UK-EU border, including Northern Ireland.
But Parliament would oversee the UK's trade policy and have the ability to "choose" to diverge from the EU rules.
Freedom of movement would come to an end but a "mobility framework" would ensure UK and EU citizens can continue to study and work in each other's territories.
What was the reaction in the Commons?
Labour leader Jeremy Corbyn said Mr Johnson and Mr Davis had abandoned a "sinking ship", shattering the "illusion of unity" initially surrounding the Chequers plan.
There was a crisis in government, he said, adding: "It is clear this government cannot secure a good deal for Britain."
Mrs May came under pressure from prominent Tory Brexiteers on the backbenches, with ex-leader Iain Duncan Smith urging her to rule out further concessions during the talks.
What has been the reaction from the EU?
The European Commission declined to comment on the resignations but Donald Tusk, the president of the European Council, said he hoped a change in faces might lead to a change in policy.
Politicians come and go but the problems they have created for people remain. I can only regret that the idea of #Brexit has not left with Davis and Johnson. But...who knows?— Donald Tusk (@eucopresident) July 9, 2018
What does it all mean for Brexit?
The UK and the EU have been negotiating Brexit terms for more than a year now and have been hoping to agree broad aims for their future relationship in October.
The aim of the Chequers away day had been to agree the UK position - after two years of discussion - but the resignations have put a question mark over that.
The uncertainty in the UK comes before the plan is officially put to the EU, who may well be unhappy with aspects of it they have previously referred to as "cherry picking".
One other element of Friday's agreement worth noting is that it pledged to speed up preparations for the UK to be ready to leave the EU without a Brexit deal in March next year.
And finally... the return of Farage?
Nigel Farage has said he will consider standing for the UKIP leadership for a fourth time when it becomes vacant in March next year, if Brexit is not "back on track" and the Chequers agreement still stands.
He backed Mr Johnson, saying the former foreign secretary had the chance to "save Brexit" by moving against the prime minister.