If Mrs May loses the vote, the government will be forced to ensure Britain remains in a customs union with the EU if no agreement on trade is reached by January 2019. 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.
The vote also demonstrated the vital importance of the four or five Labour Brexiteers who have repeatedly defied their own party whip and voted with the government.
"I don't think that she's in charge anymore", Anna Soubry complained, "I've no doubt Jacob Rees-Mogg is running our country".
Frank Field, Kate Hoey, John Mann and Graham Stringer - (plus now suspended Kelvin Hopkins) joined the majority of Tories in the voting lobby to defeat the customs union amendment, "New Clause 18".
But Mrs May suffered a setback when another rebel amendment, seeking to keep the United Kingdom in the European Medicines Agency, was passed by the Commons.
As the post-Brexit trade blueprint would see the United Kingdom abiding by European Union rules in order to have a free trade deal, it stirred outcry among Brexiteers who claimed the deal would be akin to Britain remaining in the bloc.
The Labour leader looks certain to confront her over the turmoil in Tory ranks over her Brexit plans.
In response to that, Mr Jones urged the other 27 European Union member states to "show an element of flexibility to avoid the catastrophic "no deal" scenario".
The pound was already down before the inflation data on a rallying dollar and worries about British Prime Minister Theresa May's ability to push through her Brexit plans after she only narrowly won a crucial parliamentary vote on Tuesday. Two top pro-Brexit ministers, Boris Johnson and David Davis, quit in protest last week, and a string of junior walkouts have followed suit - including two more officials on Monday.
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.
This week's votes "showed that the hard Brexit Conservatives have the numbers to sway the government's Brexit strategy, in contrast to the Rebel Remainers who have lost or withdrawan some of their key amendments".
The Green Party MP Caroline Lucas said the vote would strengthen calls for a second European Union referendum on the terms of the UK's Brexit deal.
During her visit this week, the prime minister is also due to speak to young people in Belfast about Northern Ireland's future.
"It is becoming more obvious by the day that May is finding it increasingly hard to gain a majority in Parliament for "her" Brexit plan", Commerzbank analysts said in a note.
The commission said Vote Leave had exceeded its spending limit of 7 million pounds ($12 million) by funnelling 675,315 pounds through a pro-Brexit youth group called BeLeave.