He insisted it was "not too late to save Brexit". These negotiations should be completed before the end of October to give the parliaments of both sides enough time to ratify the agreed document. "I'm looking forward to intensifying, heating up the negotiations", the new Brexit minister said in Brussels.
Earlier during Prime Minister's Questions, Mrs May said the final Brexit deal must honour the 2016 referendum result but also be "workable" in terms of protecting jobs and livelihoods.
European Union officials insist however the contingency planning for a no-deal divorce is not a sign of mistrust in the negotiations, although they admit the situation is fragile.
The plan has infuriated fervent Brexit supporters, who think sticking close to the bloc would limit Britain's ability to strike new trade deals around the world.
Aiming his remarks at European Union officials, he said what was needed was a "people's Brexit, not a bureaucrats" Brexit", in which the prosperity of citizens was placed above the "abstract ideology of the Brussels bureaucrats'.
While Johnson was delivering his speech May was along the corridor in the Houses of Parliament facing a grilling from a liaison committee, made up of every chair of every House of Commons select committee.
Shouts rang out across the Commons.
But by setting a deadline for Mrs May to change her approach, she said he appeared to be telling MPs that it would be "in their hands" if she didn't. Davis' former deputy, Steve Baker, chimed in to ask about contingency plans for a no-deal departure.
Johnson was a leading Brexiteer in the 2016 European Union referendum.
In the past 18 months, said Johnson, "it is as though a fog of self-doubt has descended".
The International Monetary Fund said on Thursday EU countries would suffer long-term damage equivalent to about 1.5 percent of annual economic output if Britain leaves without a free trade deal.
Johnson resigned from government rather than accept May's plan.
However, he said that the real aim should be "that glorious vision of Lancaster House - not that miserable, permanent limbo of Chequers". "Not the democratic disaster of ongoing harmonization with no way out and no say for the UK".
"We would need to consider what action we would take in those circumstances", she added.
"That obviously makes it very uncomfortable and some horrendous consequences, and that's what we have got to try and do our best to mitigate against".
After her 90-minute grilling at the liaison committee May faced a meeting of her backbenchers, winning support from majority.
Conservative whips, who enforce discipline in the party, threatened to call a confidence vote that could bring down the government before a crucial vote on Tuesday on customs, one lawmaker told Reuters.
So far, two other MPs have revealed that they have submitted such letters to Sir Graham since the Chequers summit - Andrea Jenkyns, MP for Morley and Outwood, and Andrew Bridgen, MP for North West Leicestershire, although a large number of others are understood to have submitted letters without revealing them in public.