But her administration was thrown into disarray within 48 hours, as first Mr Davis and then Mr Johnson said that they could not commit themselves to promote the plans under the doctrine of collective responsibility.
"On the one hand, it's true what Downing Street says", one European Union source told me.
Mr Johnson's almost two years as foreign secretary was not without controversy, with the ambitious Tory heavyweight having been accused of undermining Mrs May on more than one occasion - and making headlines for other reasons.
In the June 23, 2016 referendum, 17.4 million voters, or 51.9 percent, backed leaving the European Union, while 16.1 million voters, or 48.1 percent, backed staying. "Indeed, this work was acknowledged by the Opposition itself in Parliament", No. 6 said.
With Britain due to leave the 28-nation bloc on March 29, 2019, European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship.
British Prime Minister Theresa May dug in her heels today after the resignation of two top government ministers over Brexit negotiations whipped up a storm that threatened to topple her fragile minority government. "And how has our Government secured Gibraltar's corner specifically 24 months on?"
The senior ministers' resignations follow Mrs May's announcement of an agreement over the United Kingdom government's latest Brexit plan at Chequers.
This is a possibility, particularly now Mr Johnson has followed Mr Davis out of the door.
The HuffPost reports that May's allies believe that her unpredictable rival - perhaps the most polarising presence in the party - lacks the numbers to trigger a vote of confidence, and that "even if one was sparked, Johnson may also fail to get enough MPs needed to get his name on the leadership election ballot paper sent to party members".
The outgoing Brexit secretary said the government had gone further than it should have in the negotiations, in a "dangerous strategy".
Trump, allies set for face-off during first day of North Atlantic Treaty Organisation
He continued, "suddenly you have a situation where the USA president wants to connect the two things". At the G7 meeting, Trump reportedly said, "NATO is as bad as NAFTA", according to Axios .
And senior backbencher Bernard Jenkin said there had been a "massive haemorrhage of trust" in Mrs May.
Some Conservative Party lawmakers warned they would not tolerate a betrayal of Brexit.
Boris's resignation letter is scathing.
Addressing the backbench 1922 Committee, the Prime Minister said the alternative to the party coming together could be a left wing Labour administration.
With 316 Conservative MPs in the House of Commons, Sir Graham must receive 48 letters to call a ballot.
Asked whether May would contest a no-confidence vote, a Downing Street source said simply: "Yes".
"The prime minister knows it's a proposal and not an end agreement".
But others argued May had adopted the most realistic plan after she was weakened in an ill-judged election past year when she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern.