Ms. May has said a government defeat would weaken its hand in exit talks with the European Union.
Further votes on EU Withdrawal Bill amendments will take place on Wednesday, with no defeats expected for the government after ministers agreed a compromise wording over post-Brexit plans for a "customs arrangement". The strained parliament session underlined deep divisions over Britain's European Union exit.
It followed a strained parliamentary session, where the deep nationwide divisions opened up by Britain's vote to leave the European Union in 2016 were on display, with pro-EU lawmakers saying they had received death threats.
Just three hours later, ministers caved in.
These were the words of a minister expecting to win the vote.
British Prime Minister Theresa May narrowly avoided a major blow to her Brexit strategy Tuesday after MPs rejected a plan that would have given parliament a veto on the final deal negotiated with Brussels.
Some lawmakers tried to shout him down and accused the government of wanting too much power.
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".
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
Given that after November 30, the House of Commons looks set to be empowered in the negotiations, it would not be in Barnier's interest to negotiate a harder form of Brexit before the U.K.'s self-imposed deadline.
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In the tense atmosphere where it was not clear which way the vote would go, the government secured its victory only after offering concessions to one of the leaders of a group of Conservative lawmakers who were threatening to vote against May.
Sarah Wollaston warned that any government amendment added to the bill when it returns to the House of Lords "must closely reflect Dominic Grieve's amendment". If the compromise fails, the rebels are likely to revert back to their original motion, which would potentially strip May of control over running the Brexit negotiations and hand it to Parliament, the official said, speaking on condition of anonymity.
"Thirdly, we must under all circumstances respect the result of the referendum".
Justice minister Phillip Lee is the first minister to resign over the government's Brexit policy.
The upper chamber, the House of Lords, inserted amendments in 15 areas to soften the terms of Britain's departure.
They backed Theresa May, as they have to date on most issues, although they have previously indicated that some softer Brexit options would be acceptable as long as they didn't divide Northern Ireland from Britain in any way.
Earlier, May appeared to have also stemmed a rebellion over her commitment to leaving the EU's customs union which will transform Britain's trading relationships for decades to come.
Fellow MP Antoinette Sandbach rejected suggestions by leading Brexiteers in her party that this would tie the prime minister's hands in negotiations.
Amendment 19 would enhance the powers of parliament in the Brexit process by making a Commons vote on the final withdrawal terms a "meaningful vote".