After he sensationally quit David Davis warned the United Kingdom is giving "too much away, too easily" in the exit talks, but backed May to remain prime minister after his dramatic resignation rocked her premiership.
Chris Heaton-Harris has been appointed to the Brexit department after a raft of resignations.
May appeared in Parliament earlier on Monday afternoon to defend her plan, minutes after Downing Street confirmed the departure of Johnson.
Aside from the loyalty which MPs naturally feel towards their leader, many are concerned that Mrs May's removal could plunge the party into chaos, with no obvious replacement lined up, potentially setting the scene for Jeremy Corbyn to seize power in a new general election.
Loud applause could be heard at the end of the 1922 Committee meeting, which the PM attended for just over an hour.
To trigger a no-confidence vote in the PM, 15% of Tory MPs must write to the chairman of the backbench 1922 Committee, now Sir Graham Brady. Steve Baker also resigned as a junior Brexit minister.
The Brexit "dream is dying, suffocated by needless self-doubt", he said in the letter, which he posted to Twitter.
May says the plan will deliver frictionless trade with Europe and avoid a hard border between the U.K.'s Northern Ireland region and European Union member Ireland.
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With 11 players on the roster, the Rockets' payroll stands at $118.5 million, approximately $5.2 million shy of the luxury tax. He acknowledged that Ariza and Mbah a Moute were significant losses for the Rockets.
A successful leadership challenge would give way to a three month period of political uncertainty and domestic campaigning at a point in the negotiations where officials do not have the time to spare.
Mr David Davis replied: "Regret, really".
"It seems to me we're giving too much away, too easily, and that's a risky strategy at this time", Davis said in a BBC radio interview Monday morning.
Prime Minister Theresa May has defended her Brexit plans.
May, the leader of the Conservative party, believed she had secured a hard-won agreement with her deeply divided cabinet of ministers on Friday to keep the closest possible trading ties with the EU.
She looks set on facing down a rebellion in her Conservative Party, where hardline Brexit supporters are livid over her plans to negotiate "a free trade area for goods" with the EU.
But she told MPs: "We do not agree on the best way to deliver our shared commitments to honour the result of the referendum".
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.
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The documents say that Rocky was concerned about Johnny's volatility and called on two LAPD cops for back up. Depp's bodyguards were forced to remove the actor from the set, it is said.
But the ex-minister argued the common rule book policy "hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
What was the reaction in the Commons?
Davis and Johnson initially backed the plan, before deciding they could not support it.
The responsibility for leading the negotiations should now go to an "enthusiastic believer in your approach, and not merely a reluctant conscript", he said.
The Prime Minister is hoping to win over Tory Brexiteers after a backlash against her plans for leaving the European Union.
What has been the reaction from the EU?
Inside, the paper's report says May finds herself in a "serious crisis" caused by her "inability" to manage an orderly Brexit.
What does it all mean for Brexit?
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A legal settlement dating from the 1990s only allows the government to detain children in adult centers for a brief period. It was the first time the government indicated whether the parents and children would be released or detained together.
The value of the British pound dropped on global markets after Johnson's announcement, having risen after the announcement Friday that a Cabinet deal on Brexit had been agreed.