The government has avoided a major defeat on its Brexit bill by 324 votes to 298 after a late concession.
Ministers saw off a move to give MPs the decisive say on what happens over Brexit if they do not agree with the deal negotiated by the UK government.
The concession offered by ministers is believed to include offering a new Parliamentary motion if the Brexit deal is voted down by MPs and peers.
Two Tory MPs – Ken Clarke and Anna Soubry – voted against the government.
Five Brexit-backing Labour MPs – Ronnie Campbell, Frank Field, Kate Hoey, John Mann and Graham Stringer – voted with the government as did Kelvin Hopkins, who sits as an independent after being suspended by Labour.
The BBC’s political editor Laura Kuenssberg said she had been told by a government source that no actual concessions have been agreed and the only agreement was to keep talking.
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Tuesday’s Commons debate marked the start of the government’s attempts to undo most of the changes to its EU Withdrawal Bill that were put forward by the House of Lords.
The most contentious was the bid to give Parliament the power to tell the government what to do if the Brexit deal was voted down or no agreement was reached.
There were clashes over how much of a say Parliament should get as the UK leaves the EU, with one side accusing the other of trying to “wreck” Brexit – and being accused in turn of being “zealots” who wanted to sideline Parliament.
Seeking to placate would-be Conservative rebels, government frontbenchers offered to meet them to discuss their concerns, and agreed to “engage positively” on a “compromise” put forward by one of them, former attorney general Dominic Grieve.
Details of precisely what this will involve will be agreed in the coming days when the bill is due to return to the House of Lords and ministers are expected to table a fresh amendment.
The government blinked first
Analysis by BBC Parliamentary correspondent Mark D’Arcy
The government would not have sought a deal if it thought it had the votes to win, and they clearly blinked.
The decision to seek a compromise marked an important victory for the soft Brexit/Remainer/”realist” Tory rebels, who have been promised an amendment giving them most of what they want.
Mr Grieve said he had “confidence and trust” in Theresa May to address the concerns of more than a dozen MPs who are reported to have held last-minute talks with the prime minister in her Commons office during the debate.
Should the UK and EU not be able to agree a deal or if MPs rejected the deal on offer in the autumn, he said Parliament would have “structured input” from the end of November onwards into what happened next to try and avoid a crisis ahead of the UK’s departure on 29 March 2019.
Under the terms of his amendment, large parts of which have been accepted by ministers according to Tory MP Heidi Allen, the government would have to set out how it intended to proceed in a parliamentary motion that MPs could amend and vote on.
But the government is not believed to be willing to agree to Mr Grieve’s call for MPs to take control of negotiations in the last resort if no deal is agreed by February 2019.
Jacob Rees-Mogg, chair of the influential European Research Group of MPs. told the BBC that a concession of this kind would have been “revolutionary” as the Commons cannot override the government when it came to negotiating international treaties.
The leading Brexiteer said Mrs May had “paid attention to both sides” and the unity displayed by his party would strengthen the PM’s hand in negotiations in the run-up to June’s EU leaders’ summit.
Fellow Brexiteer Sir Bill Cash said he was pleased the Lords amendment, which he said would have given Parliament an effective veto over Brexit, had been “soundly and significantly defeated”.
‘Held to account’
Labour said the prime minister may have avoided a “humiliating defeat” but the fight to ensure Parliament had a “proper role” in shaping the outcome of negotiations would continue.
“We will wait and see the details of this concession and will hold ministers to account to ensure it lives up to the promises they have made to Parliament,” said the party’s Brexit spokesman Sir Keir Starmer.
Earlier, the government suffered its first ministerial resignation over Brexit as Phillip Lee quit the Ministry of Justice so he could speak out freely.
Mr Lee said Parliament was being sidelined and called for another referendum to be held when the final direction of Brexit becomes clear.
Revealing he had abstained in the Commons vote on Parliament’s role, he said he was “delighted” at the government’s concession, adding: “This justifies my decision to resign and makes it a lot less painful.”
The government, meanwhile, has reversed a series of other changes made by the Lords to the EU Withdrawal Bill, including reinstating the precise day of departure – 29 March 2019 – in the proposed legislation.
A government amendment on the Irish border, guaranteeing there will be no new border arrangements without the agreement of the UK and Irish authorities, was also approved by MPs.
Ministers win key Brexit bill vote after concession}