May defended her Brexit plan to lawmakers in the House of Commons on Monday, with Johnson absent from his usual place on the Conservative front bench.
But Mrs May hit back in her icy letter accepting his resignation - effectively accusing him of signing up to the Chequers plan before walking away.
The U.K.is slated to exit the European Union on March 29 of 2019, kicking off an implementation period that will run through the end of 2020. "This is the right Brexit", she said.
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. "I'd have to do something I didn't believe in", he told the BBC.
"What Theresa May was trying to do with her proposal last week was to come up with a compromise that would keep all sides on ball within the Conservative party, and clearly that has failed", Clark said.
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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.
Hunt, who served as the health secretary, was assigned to his new role late on Monday hours after Johnson handed in his resignation letter to May.
Addressing Parliament on Monday, May told MPs that she and the two ministers were at odds over "the best way of delivering our shared commitment to honoring the result of the referendum".
Davis resigned from his post Sunday evening because he said he disagreed with May's Brexit strategy.
May said the plan would deliver frictionless trade with Europe and was the "only way to avoid a hard border" between the U.K.'s Northern Ireland and European Union member Ireland.
Labour leader Jeremy Corbyn said Mrs May should make way for a Labour administration if her Government can not get its act together quickly.
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I was concentrating throughout the match, but after that penalty, it came bursting out of me". I really don't know. "They have a young, alive, attacking team". "We were lucky.
She said: 'I am sorry - and a little surprised - to receive it [resignation letter] after the productive discussions we had at Chequers on Friday, and the comprehensive and detailed proposal which we agreed as a Cabinet'.
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.
The European Commission declined to comment on Mr Davis's exit but Donald Tusk, the president of the European Council, said he hoped a change in faces might lead to a change in policy.
Johnson's abrupt departure comes two years after May took charge.
The government has battled to find a way of tackling these while maintaining access to European Union markets and avoiding burdensome customs arrangements that could damage businesses, with some leading companies warning they could cut investment or withdraw from Britain in the wake of a no-deal Brexit.
Outside of the United Kingdom, leaders have been taking a bigger picture look at the resignations. May appointed staunchly pro-Brexit lawmaker Dominic Raab as the country's new Brexit secretary.
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Now, the council has come up with another major decision of allowing students above 25 years of age to apply for NEET 2018 . However, Supreme Court had passed a judgment that students above 25 would be allowed to appear for this examination.