Crewe & Nantwich MP Laura Smith quit her job as Shadow Cabinet Office minister to vote against a Lords amendment to the EU Withdrawal Bill that would see the Government negotiate for the United Kingdom to be a member of the European Economic Area (EEA).
To avoid defeat, the government promised to make its own changes to the bill to strengthen Parliament's powers.
On Tuesday, parliament will also debate other amendments, including a challenge to the government's plan to put March 29, 2019, or "Brexit Day", into law and an attempt to toughen a commitment to ensure a frictionless border between Northern Ireland and the neighbouring Irish Republic, which will remain in the EU.
The European Union Withdrawal Bill, a complex piece of legislation meant to disentangle Britain from four decades of EU rules and regulations, has had a rocky ride through Parliament. Should lawmakers prevail, the direction of Brexit could change.
Asked for his reaction, Barnier said that he wonders if Britain "sometimes feels a certain nostalgia about leaving the European Union because it seems to want to remain inside practically everywhere without ever respecting the regulatory framework".
But while that vote seemed assured, tensions over Britain's departure from the European Union boiled over in parliament, where lawmakers from the Scottish National Party walked out in the middle of questions to the prime minister in protest at what their leader said was Scotland being ignored in the Brexit debate.
In a highly charged atmosphere in parliament, lawmakers who oppose the government said they had received death threats and brandished a copy of one of Britain's tabloid newspapers, the Daily Express, which ran a headline saying: "Ignore the will of the people at your peril". The most significant of these, which would require the government to demonstrate to parliament that it had attempted to negotiate a new customs union with the EU, is now expected to be rejected, the BBC has reported.
Mrs May met pro-EU Tories in her private room in the Commons moments before a crucial vote to hear their demands for a truly meaningful vote on the final exit deal.
A statement by the Department for Exiting the European Union, led by Brexit Secretary David Davis, insisted that "we have not, and will not, agree to the House of Commons binding the Government's hands in the negotiations".
MPs started debating the amendments to the bill just after 1pm on June 12.
On Tuesday night MPs passed a little-noticed amendment to the EU Withdrawal bill, which many MPs now believe could effectively force Britain to stay in the single market after Brexit.
Mrs May has until tomorrow to draft a legally watertight amendment to the EU Withdrawal Bill that will be acceptable to both sides. A paper laying out the UK government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.
Frank Field, a veteran lawmaker from the northwest of England, was his first victim after suggesting the point of the amendment Pennycook was backing was to stop Brexit, then Gareth Snell, who represents Stoke-on-Trent in the Midlands, got the same treatment for making a similar point.
In another day of political drama at Westminster, five Labour MPs, one of them a shadow cabinet minister, resigned from their party roles so they could defy their party managers and vote against a Labour party measure.
He added: "Can you imagine: the Government goes off to Brussels and says 'we can only discuss these three things because these are the only ones that have been covered by a House of Commons resolution".
"Parliament, don't stand against the people - implement their will!"