In his resignation letter, he argued that the prime minister's latest plan was a signal to the Brexit-voting public that the referendum was being betrayed by too soft an exit strategy from the EU.
The Prime Minister faced continued pressure over Brexit from Tory MPs during her final appearance in the Commons chamber for the summer, and will go before the Liaison Committee later.
Labour also says the June 2016 referendum vote to leave the European Union must be respected but has attacked the PM over the splits in her party.
The ex-foreign minister said he was unable to support the Chequers plan and is happy to be speaking out against it.
This is an agreement with a member of an opposite party that, as she can not attend the vote, they too will not vote so as to cancel each other out.
It comes as the new Brexit Secretary Dominic Raab faces off with the EU's Michel Barnier for the first time today - as Brussels raises threats of no deal chaos.
Mrs May narrowly survived a crunch Brexit vote in parliament on Tuesday, defeating an amendment introduced by its own backbench MPs to a future trade policy bill.
Brexit secretary David Davis and Foreign Secretary Boris Johnson resigned last week over the deal, which they said is too soft.
"We have changed tack once and we can change again".
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But his Labour shadow Barry Gardiner said: "The government's handling of Brexit over the past week has been an utter shambles. We have put forward a proposal for what the future relationship should be. and we are in negotiations on the basis of that".
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The prime minister insisted she was confident Britain had enough time to negotiate a deal with the European Union before leaving in March next year.
Boris Johnson speaks at the House of Commons on Wednesday. "We have to have a compromise position that enables the country to get an agreement with the European Union", trade minister Liam Fox told BBC radio.
Mrs May was defeated on a separate amendment to her flagship Trade Bill, which will require her to seek continued United Kingdom participation in the EU's system for regulation of medicines after Brexit.
Johnson, who led the main Brexit campaign in the 2016 referendum, resigned this month over May's strategy, triggering the government's biggest crisis since she lost her parliamentary majority after calling a snap election past year.
In a rowdy PMQs, Mrs May also accused Mr Corbyn of being "plain wrong" over his interpretation of the Government's Brexit approach before criticising the Labour leader's decision to protest against US President Donald Trump.
"It is as though a fog of self-doubt has descended", Johnson said.
Since the vote, both Mr Lewis and the Whips office, who organise the pairings, have apologised and said it was an administrative mix-up, but this argument has not convinced most people.
Ms Soubry said she did not believe Mrs May was in charge any more.
Anna Soubry's comments yesterday mirrored my suggestion previous year - that those sensible MPs - from all parties - who have been voting against the Tory Government and the Labour front bench consistently since the referendum could come together in that window after a vote of no confidence, and apply our efforts at an executive level as well as on votes in the chamber.