She's only prime minister because her predecessor, David Cameron, gambled and lost on the Brexit vote, which forced him to fall on his sword.
The Cabinet reshuffle, the way a premier can exercise ultimate power, has been a traditional device to gain strength quickly.
The Conservative former deputy PM Lord Heseltine said he believed a reshuffle was now inevitable given the prime minister's "unenviable" position - but it would be unsafe to return Mr Johnson to the backbenches. "The prospect of no deal could rise from the ashes".
But a spokesman for the Department for Exiting the European Union hit back: "The talks this week were a mutually agreed programme created to give both sides the best chance to make progress".
BAE Systems, the UK's largest defense firm, is reportedly set to announce the axing of 1,000 jobs.
The U.K. would apply the same customs duty to every country with which it does not have a trade deal or otherwise provide preferential access to the U.K. market, such as schemes for developing countries, the document said.
The plot came after her showpiece speech to the centre-right party's annual conference on Wednesday - meant to steady her leadership - was plagued by mishaps. The more time passes, the less likely they can negotiate the kind of "bespoke" transition and future close trading relationship that May says she wants. The fact that she struggled to get through her speech because of a persistent cough only amplified the sense that she is floundering.
Of Mr Johnson, whom some Conservative figures have suggested should be sacked, she said: "He is a big intellect, a big figure in the party and if the prime minister believes he is the right person to be foreign secretary then she has my full support". Claiming, also, "two good sources", Simor states that the Prime Minister had previous knowledge "that the article 50 notification can be withdrawn by the United Kingdom at any time before 29 March 2019". On Sunday, May also received strong backing from Scottish Conservative leader Ruth Davidson, who took a thinly veiled swipe at Johnson.
A team of British negotiators is heading to Brussels on Monday for the fifth and final round of Brexit talks.
This afternoon the EU Council Chief put a December deadline on talks before the bloc may have to rethink whether a Brexit deal is possible.
It has also sharpened the focus of both sides of the Brexit debate in the UK. She told ITV that Chancellor of the Exchequer Philip Hammond should be sacked for trying to "stall" and obstruct Brexit talks. However, she said in a statement that it was "patently obvious" that the EU's test of "sufficient progress" on key divorce issues were not yet met.
"To start new means for me, we need an offer from the European Union to the Brits for perhaps staying in the European Union but staying with better conditions, like a new deal".
Speaking to reporters in Maidenhead, May insisted she planned to carry on with business as usual.
May will tell lawmakers on Monday that she was offering Europe a "new, deep and special partnership" with Britain, her office said.