Mr Rees-Jogg, who as chairman of the influential European Reform Group is arguably the most influential Tory non-minister in the House of Commons, has predicted that other Conservative MPs are likely to follow his lead.
As well as Brexit Secretary Mr Davis, Steve Baker and Suella Braverman, both junior ministers in the Department of Exiting the European Union (DExEu), are also believed to have quit their posts.
Mr Rees-Mogg was quoted by Sky News as saying: “This is very important. It raises the most serious questions about the PM’s ideas.”
Comparing her deal to an egg so softly boiled that it “isn’t boiled at all”, he added: “A very soft Brexit means that we haven’t left, we are simply a rule-taker.”
Writing in the Daily Telegraph he said: “If the proposals are as they currently appear, I will vote against them and others may well do the same.’
The Chequers deal was “the ultimate statement of managing decline”, he claimed, adding: “It focuses on avoiding risk, not on the world of opportunity outside the EU.
“Pragmatism has come to mean defeatism.
“We seek a new and equal partnership. not partial membership of the European Union, or anything that…
