May's government was rocked Monday by the resignations of Johnson and Brexit Secretary David Davis.
Davis quit late Sunday saying he could not support May's plans for close trade and regulatory ties with the bloc after the United Kingdom leaves the European Union next year.
Before Johnson quit, May's official spokesman, James Slack, said Britain wanted to "move forward at pace" in the negotiations.
"In his resignation letter, Davis said 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".
But the Press Association understands that Mr Davis, who signed up to the plan agreed by the Cabinet at Chequers on Friday, has now quit.
Some euroskeptic lawmakers dream of replacing May with a staunch Brexiteer, such as Johnson, who in the past has disagreed publicly with his boss.
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"The Chequers Car Crash crosses Theresa May's own red lines, it certainly fails Labour's six tests and it is a million miles away from the kind of Brexit people thought they were getting - whether they voted Leave or Remain in 2016". In mid-afternoon trade, the pound recovered some of those losses, last at $US1.326, following the news that UK Conservative Party Chairman Brandon Lewis said he did not expect a vote of confidence against the prime minister.
Davis insisted he did not want his resignation to become a rallying cry for May's ouster.
Jeremy Hunt, who has been health secretary for the past six years, was a Remain campaigner in the 2016 European Union referendum.
"I'd have to be the champion of the policy that I didn't believe in". "That's not a tenable position".
To me, it looks like the buyers are buying the Brexit dips in anticipation of a rate hike and better economic news.
A Tory leadership contest can be called in one of two ways - if May resigns or if MPs force and win a vote of no confidence in her.
David Davis and Steve Baker clearly realised that the promises they and their colleagues made about Brexit simply can not be delivered.