Twelve rebel Tory MPs backed an amendment to keep Britain in a customs union with the EU should May fail to strike a deal with Brussels on frictionless trade by late January. Their mutiny came 24 hours after Mrs May caved in to hardline Tory Eurosceptics to back an amendment which critics says effectively kills off her compromise Brexit Chequers plan.
However, the government narrowly lost (305-to-301) a vote on the medicines regulatory regime, which means the United Kingdom will seek associate membership of the European Medicines Agency (EMA) and will in any event follow European regulation.
It was bolstered by the support of four pro-Brexit Labour Party MPs.
The close shave was May's third this week as she presents legislation on one of the most important and divisive decisions in modern British history with only a minority government, and her Conservative Party at war with itself.
Umunna said the four had helped May avoid a humiliating reverse over the customs union vote.
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Later in the day, May lost another, less symbolic, parliamentary vote called by pro-Europeans to ensure that British pharmaceutical companies would be regulated by the European Medicines Agency.
"She should do the right thing and trigger a by-election where she can, if she wishes, take her chances against a real Labour candidate".
The MP for Broxtowe told BBC Radio 4's Today programme she would be the first in the queue to give a vote of full confidence in the prime minister.
The Labour leader looks certain to confront her over the turmoil in Tory ranks over her Brexit plans. They included defence minister Guto Bebb, who quit his post in order to rebel.
The tension over Brexit spiked again Tuesday, when Britain's election watchdog, the Electoral Commission, ruled that the official pro-Brexit campaign group Vote Leave had broken the law on political spending during the 2016 referendum campaign over membership in the bloc.
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The Conservative government defeated on Tuesday an amendment introduced by its own backbench MPs to a future trade policy bill which would have kept Britain in a customs union with the EU if it fails to agree a free trade deal.
The comments came as MPs resumed debate of the Trade Bill, which is one of a series of "Brexit Bills" that intend to adjust United Kingdom legislation in preparation for when Britain leaves the EU.
Would-be rebels were reportedly warned on Tuesday that opposing the government in a vote on a customs union would lead to a vote of confidence and potentially a general election.
There is also speculation that former foreign secretary Boris Johnson could deliver a resignation speech.
The prospect of continued drama in parliament and doubts over the future of May's "white paper" Brexit plan - which is itself only a starting point for talks with the European Union - is testing the patience of businesses that depend on cross-border trade.
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As we suspected , Apple has announced an update of its two priciest MacBook Pros: the 13-inch and 15-inch laptops with Touch Bars. The new devices are available for purchase right now, starting at $1,799 for the 13-inch model and $2,399 for the 15-inch model.
While critics have said accepting the changes to the legislation mean the prime minister's recently announced Chequers deal was "dead in the water", Mrs May insisted this was "absolutely wrong" and that the changes were "consistent" with her plan.