Under party rules, 48 Tory MPs - 15% of the party's 316-strong representation in the Commons - must write to the chairman of the backbench 1922 Committee, Sir Graham Brady, to trigger a no-confidence vote.
On Friday, May seemed to have agreed a vital Brexit plan at Chequers with her cabinet. "For us that's rising odds of a general election and a delay in Brexit talks".
But in reality, she will be at the mercy of her party.
Johnson and Davis are two of the most prominent proponents of a so-called "hard Brexit", or a clean break with the EU.
PM May agreed in December that in the absence of an agreed solution to this conundrum the United Kingdom would remain effectively inside the EU's single market and customs union until one could be reached.
Only three days ago, May appeared to have agreed on a deal with her fractured Cabinet on the UK's post-Brexit relationship with the EU. He pledged to secure the "best deal with our European Union friends and partners" for the UK.
Boris Johnson has done the right thing... finally.
The move won applause from remain-supporting members of the government but heavy criticism from the minority of lawmakers who had backed leaving the European Union and wanted to see the referendum result delivered in both spirit as well as on paper.
The value of the British pound dropped on worldwide markets after Johnson's announcement, having risen after the announcement Friday that a Cabinet deal on Brexit had been agreed.
His appointment on Monday night comes amid a cabinet reshuffle by Prime Minster Theresa May following two key resignations over the ongoing row within the Conservative Party over the terms of Brexit.
The chain of resignations in the United Kingdom cabinet, which lost three of its ministers in 24 hours clearly signals only one thing - the unfolding political crisis in London, according to the diplomat."Things are covered with fog on Downing Street, while the outlines of the government crisis are peeking through it".
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