He said that felt he had to resign as he had no desire to be a "reluctant conscript" in the selling the PM's deal in negotiations with the EU. "What can the Prime Minister say to them that will actually reassure them that there will be no further concessions?"
"Where the United Kingdom chooses to apply a common rulebook, each rule will have to be agreed by parliament".
"A deal that guarantees us access to the (EU's single market) until such time as we chose regulatory divergence?..."
The proposal May will present to Cabinet on Friday - dubbed a "facilitated customs arrangement" - calls for the U.K.to use technology at its borders to determine whether goods are bound for Britain or the European Union, and charge the appropriate tariffs.
Included is a proposal to create a post-Brexit UK-EU free trade area which establishes a common rule book for industrial goods and agricultural products.
Scotland's nationalist First Minister Nicola Sturgeon, who opposes Brexit, tweeted that it "reads like cherry-picking"-but also welcomed its "realism". With those two advantages, the prime minister appears to hold her colleagues in check.
"That is not something that this country voted for, it is not what the Prime Minister promised".
His exit comes at a critical and highly sensitive time for Mrs May's strategy. It was a rare consensus, following talks at her Chequers country retreat about the way forward - a move meant to kick-start talks with the European Union that have been stalled for months.
Barnier was speaking as British Prime Minister Theresa May sought to convince her divided government to her plan for Britain's future after it leaves the European Union next March and a status-quo transition period runs out at the end of 2020. Mr Johnson's allies said on Saturday he decided not to quit as he wanted to remain in government to fight for the kind of Brexit he campaigned for.
It claims the Prime Minister's Brexit promises appeared to be "a pretence and a charade meant to dupe the electorate" and concludes that "in the interests of our country and the future of the Conservative Party, I feel the time has come for a new leader". Some lawmakers have already expressed their misgivings.
Jacob Rees-Mogg, the leader of the eurosceptic European Research Group (ERG) of Conservative MPs, refused to condemn the plan outright.
But as Monday drew to a close, May was cheered and applauded by many Conservative lawmakers at a private meeting, having earlier spent more than two hours in parliament answering sometimes hostile questions.
He added: "All those of us who believe that we want to execute a proper Brexit, and one that is the best deal for Britain, have an opportunity now to get behind the Prime Minister in order to negotiate that deal".
Conservative former minister John Redwood asked Mrs May to "clear away the ambiguity or contradictions in the Chequers statement which implies we would give the ECJ powers, we might pay money to trade and we might accept their laws and we might have their migration policy".
Brexiteer Cabinet minister Michael Gove admitted the plan was not everything he had hoped for, but he was a "realist" and the Prime Minister's lack of a Commons majority meant the "parliamentary arithmetic" was a factor in deciding what could be adopted.
Theresa May has shown strength and courage in facing down Tory Brexiteers to get Cabinet agreement on pursuing a de-facto single market in goods with the European Union after Brexit without so much as a squeak from Ministers.
While full details of Mrs May's plan have yet to be revealed, backbench Brexiteers are struggling to digest what has been published thus far. "It was the right thing to do".
Andrea Jenkyns said Mr Davis' departure was "fantastic news" and hailed Mr Baker as "another courageous and principled MP". I take my hat off to you.
"Just as when we sign trade deals with other parts of the world, we will need to ensure that both sides operate to the rules appropriate there".