She said: "I am sorry that you have chosen to leave the Government when we have already made so much progress towards delivering a smooth and successful Brexit and when we are only eight months from the date set in law when the United Kingdom will leave the European Union".
In his first speech to the House of Commons since resigning, where he was flanked by supporters including Davis, Johnson said May could still change course.
Amid rising backbench anger, MPs are set to vote today on a series of Commons amendments meant to wreck her Chequers plan for a "common rule book" covering a new "UK-EU free trade area".
He also called for Theresa May to tear up her "miserable" plans for close relations with the European Union after Brexit and return to the "glorious vision" of Global Britain which she set out previous year.
However, in a sign of just how volatile the party has become, former education secretary Justine Greening - who backed Remain - denounced the plan, saying it offered the "worst of both worlds" and called for a second referendum.
"If we don't, we risk ending up with no Brexit at all", she said.
"It is time for all of us - at this critical moment in our constitutional development - to believe in ourselves, to believe in the British people and what they can do, and in our democracy", he wrote.
"That was the vision that the Prime Minister rightly described a year ago".
In a series of votes, May could come under attack from arch-Brexiteers in her own Conservative Party who think her plans have watered down Brexit and will leave Britain shackled to the European Union once it leaves the bloc in March.More news: Top Chelsea star reportedly agrees to join Real Madrid this summer
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Johnson told lawmakers that the government had "dithered" and failed to make the case for a free trade agreement outlined in the January 2017 speech at Lancaster House in the heady months after the referendum passed.
"We must try now because we will not get another chance to do it right", he said.
"Not the democratic disaster of ongoing harmonisation with no way out and no say for the UK".
Johnson demanded Britons "believe in this country".
Conservative infighting must end and a consensus found on a sensible, practical Brexit.
Bannon's remarks come shortly after Donald Trump, in an interview with the Rupert Murdoch-owned Sun newspaper published hours before he was due to meet May, directly criticised May's Brexit strategy and heaped praise on Johnson, saying he "would be a great prime minister".
However, a close ally of Philip Hammond, the Remain-backing Chancellor, mockingly described talk of crisis over the Chequers plan as "fake news", adding: "Crisis?"
Pro-EU Tory Phillip Lee, who quit as a minister over Brexit, condemned any thought of an earlier break as "shameful" at a "crucial time".
Mrs May's white paper would restrict ministers' powers to initiate, innovate or deviate from the Brussels rule book to the extent that they would never again be able to institute a reform programme of the type introduced by Margaret Thatcher in the 1980s, he said. "I have come to the conclusion that.it is not what people voted for".