Mrs May looked as if she could have been defeated by a key amendment in the European Union withdrawal bill- known as the meaningful vote- introduced by the House of Lords, which would have given parliament powers to direct the Brexit negotiations.
The concession came after intensive horse-trading on the floor of the House of Commons, with chief whip Julian Smith shuttling between Tory backbenchers during debate on Lords amendments to the EU Withdrawal Bill. He said that while he was sad to leave the government, he believed many big changes were needed to make the U.K.'s exit a success.
"I promised Crewe & Nantwich that I would respect the referendum result".
Rebels had been pushing for an amendment that would have given Parliament unprecedented powers over the final stages of Brexit talks. "It's not practical, it's not desirable and it's not appropriate", Davis said.
By Tuesday evening, May was able to avoid a backbench parliamentary revolt, conceding that if her government fails to secure a Brexit deal by November 30, 2018, she will return to the House that will decide "what happens next". Several pro-EU Conservative lawmakers said they would join the opposition in voting against the government.
The pro-European cause was boosted when junior justice minister Phillip Lee, a close personal friend of the prime minister, resigned shortly before the debate in order to back the veto amendment. 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 change reduces the likelihood that Britain could leave the European Union without a deal if it does not like the divorce terms.
"Secondly, we can not change the fundamental constitutional structure which makes the Government responsible for global relations and worldwide treaties".
MPs started debating the amendments to the bill just after 1pm on June 12.
May objected to the amendment - inserted by the House of Lords - because she said it would tie her hands in the negotiation.
But Brexit campaigners feared it could weaken Britain's negotiating stance in talks to leave the European Union and the Brexit ministry was quick to put out a statement saying: "We have not, and will not, agree to the House of Commons binding the government's hands in the negotiation".
Parliamentary debates about complex legal amendments rarely rouse much heat, but passions run high over anything to do with Brexit. The Daily Express thundered: "Ignore the will of the people at your peril".
Following days of frantic lobbying by Conservative officials, May renewed appeals for unity over the "meaningful vote", after the government appeared to have secured a compromise to stop a similar rebellion on Wednesday over Britain's trading ties with the EU.
She told the Commons: "The central choice for Parliament is whenever we accept the outcome of the referendum or do we seek to subvert that process?"
Umunna, MP for Streatham, said: "Curbing Commonwealth immigration then and ending European Union free movement now did and is not going to solve these problems and we know it".