The meaningful vote is probably the most risky of the Lords amendments to the EU (Withdrawal) Bill - because it tees up an unpredictable vote on the final terms of Brexit, towards the end of this year, and opens up the possibility that MPs could demand that ministers change policy, in the event the terms were rejected by the House, or no deal was reached in the talks with the EU.... they could even demand (drumroll) a second referendum...
Government sources signalled to the Press Association that ministers were set to back the move.
It followed a strained parliamentary session, where the deep divisions opened up by Britain's vote to leave the European Union in 2016 were on display, with lawmakers who oppose the government saying they had received death threats.
She insisted: "We must think about the message Parliament will send to the European Union this week".
"The time has come for our elected representatives to decide - are you or are you not the servants of the people?"
Britain's highest-selling tabloid, The Sun, which is owned by Rupert Murdoch, addressed lawmakers directly on its front page, saying they faced a choice between "Great Britain or Great Betrayal".
Appearing before the 1922 Committee of backbench MPs, Mrs May argued that the party had to stay united to strengthen her negotiating position in Brussels.
After the vote, Grieve told the Guardian: "I am very pleased that the government has listened to the concerns of many colleagues and has responded positively to the need to amend the bill further to provide a proper mechanism to enable parliament to act, where necessary, if there is no deal or a deal is rejected by negotiations". If and when agreement can be reached, the new amendment will be introduced in the House of Lords, when the bill returns there in the next stage of its passage through parliament.
The E.U. (Withdrawal) Bill is the draft law that would set the legal framework for Brexit and Ms. Conservative MPs keen to retain the changes.
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Some pro-EU Tories were reported to be backing away amid fears Mrs May could be fatally damaged by defeat, opening the way for a hardline Brexiteer to take over at the top of the party.
Dominic Grieve tabled an amendment last night which forced the government's hand over the issue of a meaningful vote.
Ministers had instead suggested an amendment meaning that ministers should have 28 days before having to come to the Commons with a back-up plan, and would then make a statement setting out how the government proposed to proceed. "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", he said.
"A vote between bad and worse is not a meaningful vote".
The government won the vote after last-minute horse-trading, some of it in the open on the floor of the House of Commons - some behind closed doors.
Earlier, Brexit minister David Davis told parliament a defeat would undermine negotiations with Brussels and warned lawmakers the government would never allow them to "reverse Brexit".
"The people want us to leave the EU".
Labour and Conservative MPs are bitterly split over Prime Minister Theresa May's desire to keep Britain in the European Economic Area.
Parliament will vote Tuesday on a key piece of legislation, the E.U. Withdrawal bill, that would transfer European Union laws now on British books into British law after Brexit.