Britain's Foreign Minister Boris Johnson leaves 10 Downing Street in London, Wednesday, June 13, 2018.
Dr Lee, who supported the campaign to remain in the EU, said: "When MPs vote on the House of Lords" amendments to the EU Withdrawal Bill I will support the amendment which will empower Parliament to reject a bad deal and direct the Government to re-enter discussions.
As a result, they withdrew their objections and voted with the government, sparing May an embarrassing defeat.
But the rebels were split, with 74 voting in favour of the Lords amendment, which called for the Government to pursue the so-called "Norway Model" membership, and 15 against it.
May and her ministers renewed appeals for unity over the "meaningful vote", after the government appeared to have secured a compromise to quell a potential rebellion on Wednesday over Britain's trading ties with the EU.
Two of the putative rebels, Anna Soubry and Heidi Allen, quickly said that did not match their recollection of what had been promised, with Soubry urging the government to "sort it please".
"If the PM goes back on that there will be no agreed amendment that I can support #sortitplease".More news: Markets fall after Beijing accuses Washington of 'blackmail'
Speaking at prime minister's questions, May said the government meant to bring forward its own amendment, but stressed that she could not allow MPs to bind the government's hands or to open it up to the risk that Brexit could be reversed.
But it came at a cost - a government promise to strengthen Parliament's voice, potentially at the expense of its own power to set the terms of any final divorce deal with the EU.
"I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible", she said.
"Our policy is to leave the customs union so we can conduct our own independent trade policy, but it would be appropriate to have an arrangement in place", Baker told reporters. However, with the vast majority of both Leave and Remain voters agreeing that the government's negotiating strategy has been a failure, MPs across the aisle have started to have doubts about whether a satisfactory deal will be possible. The government should be investing more in housing, the health service and education to relieve pressure on services, he said, not ending free movement of labor.
Dr Lee's shock departure came as Brexit Secretary David Davis warned potential Tory rebels that they can not undo the European Union referendum, ahead of a tricky 48 hours in which the Government will try to get its Brexit programme back on track.
An alternative compromise tabled at the 11th hour by former attorney general Dominic Grieve would require ministers to get Parliament's approval for their next steps if no political agreement has been reached with the European Union by the end of November.
"The question of what form parliamentary approval of the withdrawal bill takes is one of the most significant decisions this house will have to take", he said.More news: England World Cup game beats royal wedding in TV ratings
The front pages of Leave-backing British newspapers said accepting the amendments would betray the 52 percent who backed Brexit in the seismic 2016 referendum.
"There's a reasonable expectation that something will emerge, but I need to work on that and more importantly work with colleagues to come up with something".
Leading pro-EU Conservative Sarah Wollaston said the "promised further amendment" in the Lords must "closely reflect" the withdrawn proposal.
Perhaps the most significant compromise from Mrs May was on what happens if there's no deal. How does parliament have a say in those circumstances?
She added: "I can not countenance parliament being able to overturn the will of the British people".
Another Conservative Remainer, former Cabinet minister Nicky Morgan, denied that the rebels had been "played" by the Prime Minister.
"I don't think that's right", she said.More news: Rapper XXXTentacion shot dead in Florida
- Prince Harry and Meghan Markle have confirmed they're visiting Ireland next month
- OnePlus 6 Hits Record Sales, Rewarding India Customers with Cashback and More
- Fan rushes to scene of XXXTentacion's death
- Allies unhappy with United States walkout from UN body
- James Rodriguez makes belated start for Colombia
- Plane carrying Saudi Arabia's World Cup team catches fire
- Supreme Court closes online sales tax loophole
- Why Didn't Kate Middleton, Prince William Attend His Cousin's Wedding?
- Minister: S. Korea 'flexible' on timing, format of ending Korean War
- Disgraced ex-FIFA president Sep Blatter arrives in Russian Federation for World Cup