Facing the prospect of losing a vote on a crucial amendment to the government's flagship Brexit legislation - which was created to empower parliament to vote down the final deal without risking a "no-deal" exit from the bloc - ministers intervened with a concession at the 11th hour even as MPs were wrapping up debate on the controversial measure. The strained parliament session underlined deep divisions over Britain's European Union exit.
Ahead of the vote on Tuesday, Justice Minister Phillip Lee resigned, saying he could not support the government's position.
Remain-supporting Conservative MPs had threatened to defeat the government on an amendment known as the "meaningful vote" amendment, which would have given Parliament a wide-ranging veto to May's Brexit deal, or even bring about another referendum on whether Britain should leave the EU.
Mr Grieve said no government would survive if it tried to dispense with Parliament's input.
He said: "I understand the difficulties MPs representing constituencies which voted strongly for Leave or Remain have on the EEA amendment to the EU Withdrawal Bill".
The vote was one of the most important in two days of votes that began Tuesday on the government's EU Withdrawal Bill.
The fall-out from Britain's referendum vote in 2016 to leave the European Union has reshaped politics, deepening divisions within its main parties and raising tensions between its four nations - England, Scotland, Wales and Northern Ireland.
The BBC's political editor Laura Kuenssberg said she had been told by a government source that no actual concessions had been agreed and the only agreement was to keep talking.
After Mrs May talked round potential rebels, MPs voted by 324 to 298 to reject a House of Lords amendment that would have given Parliament the power to tell the PM to go back and renegotiate the Brexit deal she secures from Brussels.
The move was branded "sneaky" by one backbencher while another senior pro-EU Tory said the wording of a Government amendment was changed at the last minute to deny MPs the chance of blocking a "no deal" Brexit.
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On Tuesday the battle for control came to a head, as lawmakers geared up to vote on whether to provide a "meaningful vote" to Parliament, something that could pave the way for a second referendum.
Keir Starmer, the main opposition Labour's chief Brexit spokesman said: "The government's amendment is simply not good enough". Should lawmakers prevail, the direction of Brexit could change.
The British government has faced fierce criticism both at home and by the European Union for its lack of clarity on its Brexit strategy.
May's officials begin work on Wednesday, drafting a new clause in her key piece of Brexit legislation after she narrowly avoided a defeat in Parliament by offering last-minute concessions to pro-EU lawmakers.
Pro-Brexit politicians argue that staying in an EU customs union would limit Britain's freedom to trade with other countries.
UK Prime Minister Theresa May is in a frantic search for the ideal compromise.
Mrs May has made an art of holding together the factions in her divided party, but it remains to be seen if she can find an amendment that prevents a rebellion from either side.
The row centres on what say parliament will have over any final Brexit deal agreed with Brussels.
He said Mrs May had promised to table a fresh amendment based on his own proposal for Parliament to be consulted on the way forward if no deal is agreed by the end of November.