But in extraordinary scenes, ministers were forced to offer last-minute compromises to pro-European MPs before holding private talks in corners of the chamber as the debate raged on.
Theresa May ultimately persuaded all but two of her MPs to back her in the decisive vote in Westminster on Tuesday - but she increasingly appears little more than a hostage to the warring factions in a bitterly divided Conservative party.
The Prime Minister is now expected to get through the latest round of crunch Brexit votes unscathed, with a potentially explosive clash over the customs union on Wednesday already defused by a compromise amendment.
The final vote, as outlined in Grieve third point, would be different as the government would then have to follow any direction given by the Commons.
May is resisting changes approved by the House of Lords that would soften Britain's exit from the European Union, because she says they will weaken the government's negotiating position.
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Intensive talks will continue between both sides in the run up to the European Council summit on June 28, where leaders hope to make significant progress towards a solution to the Irish border issue. The European Union Withdrawal Bill, meant to enact Britain's exit from the bloc, has had a rocky ride through Parliament.
Among the 14 amendments to the Bill - set to be voted on by MPs on Tuesday and Wednesday - are changes which would see the United Kingdom stay in the Single Market and would allow Parliament to dictate future negotiating terms.
It is believed the deal will see parliament playing a bigger role in Brexit negotiations if there is no deal by November 30 this year. The victory was Pyrrhic, as the government's earlier climbdown all but ensures MPs will have an increased say on the terms of any deal.
British Prime Minister Theresa May is urging feuding Conservative lawmakers to unite and prevent the government from being defeated in key votes on its main Brexit bill.
However, this has not been enough to satisfy the concerns of Tory rebels, leading to the further concessions made. "We have no doubt of what was going on".
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Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give Parliament the voice I always wanted it to have in the Brexit process".
A spokesperson for the Department for Exiting the European Union said: "On the meaningful vote we have agreed to look for a compromise when this goes back to the Lords".
His pro-European colleague Anna Soubry hit back that hardline eurosceptics were seeking to "take us over the cliff of hard Brexit".
But Solicitor General Robert Buckland publicly implied that Government would be accepting part of Grieve's amendment, and said that a "structured discussion" would take place with rebels.
Opposition Labour lawmaker Chuka Umunna had earlier accused Britain's tabloids of intimidation, holding up Tuesday's edition of the eurosceptic Daily Express.
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