The "meaningful vote" is a crucial amendment passed in the House of Lords which, if passed in Commons, would have allowed Parliament to take charge of the negotiating strategy if they vote against the Government's Brexit deal in autumn.
"We had a personal assurance that we would find a way of addressing the concerns which are encapsulated in these amendments", Mr Grieve said as voting continued on Tuesday.
But pro-EU Conservative lawmaker Dominic Grieve said that with the government's move "I am quite satisfied that we are going to get a meaningful vote on both "deal" and "no deal" scenarios. "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.
In a concession, the government promised that lawmakers would have a say on what to do next if there is no agreement with the European Union, or if Parliament rejects the deal offered.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
Earlier May suffered a setback when junior justice minister Phillip Lee, who has always been critical of Brexit strategy, resigned and said he would vote against the government.
"This justifies my decision to resign and makes it a lot less painful".
MPs voted down the Lords amendment on "sifting regulations" by a majority of 22.
During Tuesday's debate, Ms Soubry told the House of Commons that a fellow Remainer MP had to be guarded by six armed undercover police officers at a recent public event.
See How Pete Davidson's Ex Girlfriends Responded to Ariana Grande Engagement Bombshell
What is even more shocking is that the two of them announced their engagement 20 days after confirming their relationship.
The government says the changes would weaken Britain's negotiating position and is seeking to reverse them in the Commons.
Conservative Brexit campaigners accused those in the party who indicated they would vote against the government of not respecting the referendum result.
But while the well-worn arguments focusing on the nature of a meaningful vote were made, the real drama was taking place on the floor of the chamber where chief whip Julian Smith, solicitor general Robert Buckland and Brexit secretary David Davis as well as the Prime Minister's parliamentary private secretary (PPS) George Holingberry were in deep discussion with each other and Grieve, as they sought to avert an embarrassment for the government.
They reassured anti-Brexit MPs that the government would accept some of their core demands to give parliament a meaningful say on the terms of Britain's European Union divorce, including - potentially - a new deadline for a deal to be agreed with Brussels that could make it hard for the government.
The U.K. voted to leave the political and economic bloc of 28 nations in June 2016. "That's what this House voted on Article 50".
Earlier, a junior minister resigned to fight for a "meaningful vote" for MPs, saying the government was offering a "fake choice" between "a bad deal and no deal".
He said: "Facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".
Details of precisely what this will involve could emerge in the coming days when the EU Withdrawal bill is due to return to the House of Lords.