This comes following theresignations of David Davis as Brexit secretary and Steve Baker as a junior Brexit minister - with fieldwork for the poll finishing just prior to the further resignation of Boris Johnson as foreign secretary.
But as Mrs May set about trying to steady the ship, a senior Cabinet minister told the Express & Star there was "absolutely no appetite" in the Tory ranks for another leadership battle.
On Tuesday morning Theresa May held her first cabinet meeting after the reshuffle. They would then need the votes of at least 159 MPs to actually get rid of her.
"The prime minister knows it's a proposal and not an end agreement".
"Two secretaries of state have resigned and still we are no clearer as to what our future relationship with our nearest neighbors and biggest trading partners will be".
"There is absolutely no appetite for a leadership battle".
He has served as health secretary since 2012.
In what amounted to a declaration of political war, Johnson said May's vision of a close future relationship with the European Union would confine the United Kingdom to a "status of colony" and amounted merely to a "semi-Brexit". I have met many people with different views.
Fellow Tory Brexiteer Peter Bone welcomed Mr Davis's resignation, saying it was "a principled and fearless decision", while Andrea Jenkyns said Mr Davis's departure was "fantastic news" and hailed Mr Baker as "another courageous and principled MP".
"He added life and colour. He prefers the broad picture, the principles, rather than the minutiae", he said.
Mr Fabricant lauded Mrs May's Brexit plan as a "pragmatic compromise".
The UK economy continued to pick up in May after the slowdown seen in Q1 amid the boost in service sector growth, while manufacturing and industrial activity data disappointed.
She told Sky News: "I'm happy to hear it will be published on Thursday".
The Prime Minister's latest political drama began late on Sunday night when Davis announced his decision to leave his post, declaring he could not support May's plan for Brexit agreed plan.
"Over the coming days, weeks and months these negotiations will become more intense as we head towards leaving the European Union on March 29, 2019".
Opposition Labour Party leader Jeremy Corbyn said the government was incapable of delivering Brexit. And she was given a reprieve tonight with news she will not face an immediate vote of no confidence.
Hunt supported Remain during the 2016 referendum on EU membership, but has since been critical of the European Commission's approach to negotiations.
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