It sets up the prospect of frantic efforts by Mrs May to appease both Leave and Remain sides of her parties, as well as another potential crunch vote in the House of Commons next week.
The Government has avoided a major defeat on its Brexit Bill after a last-minute concession, Tory rebel Dominic Grieve explains just exactly what the concession was.
"Labour will only vote for a final Brexit deal if it delivers a strong relationship with the single market based on full tariff-free access and ensures no loss of rights and standards", Labour leader Jeremy Corbyn said on Facebook.
Opposition Labour lawmaker Chuka Umunna had earlier accused Britain's tabloids of intimidation, holding up Tuesday's edition of the eurosceptic Daily Express. The news they all voted against is no surprise, as the party supports not leaving the European Union altogether.
But after meeting Mrs May he told this paper: "I've been to see the prime minister and received important undertakings and made a decision to vote to give the prime minister the authority and freedom to negotiate the best deal she can". The government fears a weakened negotiating position.
As time ticks by, May can no longer kick decisions down the road, increasingly under pressure from European Union negotiators to come up with detailed positions not only on customs, but also on future trade relations and governance.
Further ahead, there is the growing possibility of MPs forcing another referendum or a snap election on the eventual Brexit deal.
Remain-supporting Conservative MPs had threatened to back an amendment to the bill which would have given parliament a more widespread veto.
Rebels had been pushing for an amendment that would have given Parliament unprecedented powers over the final stages of Brexit talks. But a government official said they had just agreed to open talks on the basis of the rebel amendment.
Brexit Secretary David Davis urged MPs to "respect the result of the referendum" that approved the withdrawal.
But the cabinet's anxiety about the nail-biting parliamentary arithmetic increased significantly after the resignation of Bracknell MP Phillip Lee, who left his post on Tuesday morning to free his hand to vote against the government.
The House of Lords has inserted 15 amendments to soften the terms of Britain's departure.
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.
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. - After a rollercoaster week of Brexit rows within her government and with Brussels, British Prime Minister Theresa May will on Tuesday seek to avoid another setback in a long-awaited showdown with parliament.
Ms. May's minority government relies on the support of Northern Ireland's Democratic Unionist Party for a slender working majority in the 650-member Commons.
Either way, the chances are increasing that Parliament will get a greater say over Brexit.
"The decision was taken by the people, we gave them that decision and we have to stand by it", said Conservative MP Bill Cash.
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