The BBC reports that defence minister Guto Bebb "resigned so he could vote against the government", adding yet another minister to the growing list of resignations.
The House of Commons voted against an amendment to the Trade Bill which would have forced the prime minister to pursue a full customs union with the EU if she has failed to secure frictionless trade by January 2019.
With an ever-diminishing majority the United Kingdom government has resorted to drastic measures, proposing that parliament closes five days earlier than usual.
Commons sources said the Government is going to bring forward a motion to end the parliamentary term early on Thursday, ditching plans to sit on Monday and Tuesday next week.
The Trade Bill is focused on converting trade deals between the European Union and third countries into bilateral deals with Britain.
"It's nothing more than a shameless attempt to evade scrutiny by a government in absolute disarray", said opposition lawmaker Matthew Pennycook, a member of the Labour Party's Brexit policy team.
Mrs May bowed to Brexiteer demands earlier to stem a threatened uprising on the Customs Bill.
The prime minister also said that the taxation (cross border trade) bill, which seeks to allow the United Kingdom to implement its own customs regime after Brexit, and a related trade bill on Tuesday, were "an important part of our no-deal preparations" because both were necessary to prepare the United Kingdom for life as an independent trading nation.
She said: "The universal truth is that the Chequers would not have been accepted by the European Union".
Amid all the upheaval, a second referendum still seems unlikely.
One of the amendments forces the British government to commit itself in law not to allow a customs border down the Irish Sea - a move that potentially rules out the EU's "backstop" on customs.
Applying EU tariffs to products destined for the EU is part of Mrs May's plan to avoid friction at United Kingdom borders after Brexit.
May's government is defeated on an amendment committing the United Kingdom to retaining European Union regulations on medicines.
Three Labour MPs voted with the government. The government was defeated by four votes, 305-301, then won the more important customs vote 307-301.
In a sometimes heated debate Conservative Anna Soubry said the plan May agreed at her meeting with ministers at her Cheqeurs retreat had now been wrecked by caving in to no-deal Brexiteers.
Eurosceptic Conservatives are planning to vote against the government on several amendments to the trade bill.
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