Her spokesman said she had welcomed the new members of her cabinet and they had discussed the publication of a white paper policy document on Britain's future ties with the European Union and stepping up preparations for any no-deal outcome to the negotiations with Brussels.
After being the surprise pick as foreign secretary, Mr Johnson's gaffes did not cease.
On Monday, high-profile Brexiteer and Conservative MP Johnson announced he was resigning from the Cabinet, following the agreement of a Brexit proposal that would see the United Kingdom retain close links to the European Union after exiting the organisation.
Although it has caused a headache, May was quick to capitalize on the fact that two of her biggest problems extricated themselves from her inner circle; she ceremoniously replaced Davis and Johnson with more amiable substitutes.
Some Conservative Party lawmakers warned they would not tolerate a betrayal of Brexit.
"He's been very, very nice to me, very supportive", Trump said.
Johnson quit with a resignation letter accusing May of flying "white flags" of surrender in negotiations with the European Union.
Party rules dictate that 48 Tory MPs - 15% of those in Parliament - must sign letters of no confidence to trigger a vote, but that number has not yet materialised.
Eight boys rescued from Thai cave in good mental, physical state
The rescuers have been learning from experience and were two hours faster in bringing the second batch of survivors out on Monday. Manchester United is greatly relieved to learn that the 12 footballers and their coach trapped in a cave in Thailand are.
Aside from the loyalty which MPs naturally feel towards their leader, many are concerned that Mrs May's removal could plunge the party into chaos, with no obvious replacement lined up, potentially setting the scene for Jeremy Corbyn to seize power in a new general election.
This has resulted in the Daventry MP becoming the Parliamentary Under Secretary of State, replacing Mr Baker.
Less than nine months remain until Britain reduces the EU's membership on March 29, 2019.
Asked if the PM lives to fight another day after the meeting, Mr Buckland said: "Oh, definitely. The Prime Minister thanks Boris for his work".
Boris Johnson has done the right thing... finally.
In June this year he urged Mrs May to deliver a "full British Brexit", and not something that was "half-hearted".
The newly appointed foreign secretary was previously the longest-serving health secretary in history and is seen as a stable figure in May's government, maintaining a "studious loyalty to the prime minister throughout her current difficulties", The Independent says.
In a pointed message, the president of the European Council Donald Tusk appeared to suggest that the resignations could spell the end for Brexit.
But others argued May had adopted the most realistic plan after she was weakened in an ill-judged election a year ago when she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern. Nobody would assume they would go in and walk out with the same agreement.