Theresa May has triggered fury from Conservative remainers after caving in to pressure from pro-Brexit Conservative MPs to accept a series of rebel amendments to her customs bill.
Eurosceptics will have a chance to show their strength in the House of Commons later Monday by voting on amendments to a bill setting up May's new customs regime after Brexit.
MPs voted by 305 to 302 to support an amendment to the Trade Bill that seeks to unpick a key plank of the Prime Minister's plans for a "soft" exit from the EU.
"I have come to the conclusion that it does not respect the referendum result - it is not what people voted for", he said.
Some MPs are planning to vote for amendments that would tie Britain to a permanent customs union with the EU.
A Labour source told HuffPost: "Theresa May sounds like she is running scared of her own MPs".
Another pro-EU lawmaker Dominic Grieve, who has led previous efforts to get the government to soften its Brexit stance, said the party needed to accept compromises "or accept that Brexit can not be implemented and think again about what we are doing".
The controversial plans, which detail "a common rule book" covering a new UK-EU free trade area, were presented by Mrs May as a hopeful compromise approach in Brexit talks.
"I wanted the prime minister's Chequers agreement to be a workable compromise", she wrote in The Times.More news: Frank Sinatra's first wife Nancy dies aged 101
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Asked if there was a suggestion that ministers would accept the amendments he said: "No".
The prime minister also said that the taxation (cross border trade) bill, which seeks to allow the United Kingdom to implement its own customs regime after Brexit, and a related trade bill on Tuesday, were "an important part of our no-deal preparations" because both were necessary to prepare the United Kingdom for life as an independent trading nation.
Greening, a former Education secretary who quit May's government in January, is the highest-profile Conservative to support a second vote, though she was not an advocate of leaving the E.U.in the first place.
In one of the rowdiest debates in parliament on Brexit so far, pro-EU Conservative lawmaker Anna Soubry said: "The only reason that the government has accepted these amendments is because it is frightened of somewhere in the region of 40 members of parliament, the hard no-deal Brexiteers, who should have been seen off a long time ago".
Greening said she would campaign to keep Britain in the European Union, if a new referendum were held.
"What we need is a clear route forward that settles this European question once and for all".
Pro-Europeans also dislike May's plan, particular her goal to have looser ties with the European Union for Britain's dominant services sector.
He told Today: "The amendments are to a Bill that is created to prepare for the world after Brexit, to be able to establish new customs regime that will be necessary".
Amid all the upheaval, a second referendum still seems unlikely.