Mr Johnson said: "It's vital that all MPs are able to air their views on Brexit".
"One former Tory leader, Sir Robert Peel, made a decision to break his manifesto pledge and passed legislation with the majority of his party voting the other way".
"At least he did so for a policy that works".
Business minister Richard Harrington and two foreign office ministers - Sir Alan Duncan and Alistair Burt - all rounded on him for his comments.
Simon Hoare, MP for North Dorset, took to Twitter to tell Rees-Mogg: "The hectoring nonsense / blackmail has to stop, the reality of parliamentary arithmetic dawn and the calamity of a Corbyn Government woken up to". The prime minister insisted, however, in answers to questions from pro-European Tory MPs, that she would deliver a deal that met the concerns of businesses.Drawing jeers from some Brexiteers Nicky Morgan, the Tory chairwoman of the Treasury select committee, asked Mrs May to "do what Conservative prime ministers over the ages have done" and find a "pragmatic, sensible and flexible Brexit".
The influential Brexiteer has written a column for the Telegraph newspaper in which he appears to make a veiled threat to the Prime Minister.
Briefing Cabinet ministers ahead of the Chequers talks, Oliver Robbins is said to have painted a bleak picture of the situation, with a source telling The Times they came out of the meeting thinking "we were even more screwed than we were before".
While unacceptable to Brussels, the prime minister's plan also risks provoking hardline Brexiteers in her own party, who argue that effectively staying in the single market for goods will leave the UK's hands tied when it comes to negotiating any future post-Brexit trade agreement. Firstly, the new customs partnership (NCP), where the United Kingdom stays within the European Union customs system and collects tariffs on Brussels' behalf. The second option, known as "max fac", or maximum facilitation, would implement a technology-based plan.
Both options have been dismissed by the EU.
Britain's Secretary of State for Environment, Food and Rural Affairs Michael Gove talks about the planned cabinet meeting, at the Prime Minister's official country residence Chequers later this week, on the BBC radio Today programme in London, Britain, July 4, 2018.
"Now, with the time running out ahead of the UK's exit from the European Union, business patience is reaching breaking point".
But both leaders only laughed when asked by waiting reporters if the European Union would support May's reported proposal of a third option for overcoming the hard issue of what customs arrangements to adopt after Brexit.
Mrs May said next week's Government's white paper would set out "detailed proposals for a sustainable and close future relationship" between the United Kingdom and European Union and mark "an important step in delivering the decision of the British people".