The defeat - over ensuring the political, social and economic rights protected by the European charter of fundamental rights are replicated in British law - follows a vote by the Lords that challenged May's plan to leave the customs union, which increased pressure on the prime minister to reconsider. "But clearly they won't do that as long as they think Parliament will vote for a customs union".
Appearing before the MPs on Wednesday, the Brexit secretary was asked what would happen if the Commons voted in favour of a "meaningful amendment" to the proposed agreement that instructed the government to "go back and get another deal".
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The Customs Union is concerned with the consent of all members of the Union to apply the same taxes on imports of goods from outside the Union.
Britain's upper house of parliament handed the government its third defeat over Brexit in less than a week on Monday, voting down plans not to retain European Union rights in national law before Britain leaves the bloc.
The EU's chief Brexit negotiator has told businesses to prepare for the possibility of the United Kingdom exiting the bloc without a transition period amid a stalemate over the Irish border issue.
"I am not going to speculate what government will do in response to an amendment which has not yet been laid let alone passed by the House."
It is understood that the customs union is not on the formal agenda, but the issue is expected to test Cabinet unity in the coming weeks, with senior Brexiteers like Boris Johnson and Liam Fox understood to be wary of any concession.
However, the issue is not on the agenda for the meeting, sparking concerns from senior ministers that discussions will.
That will be put to the test again next week as MPs debate the customs union and the next round of Brexit negotiations take place in Brussels.
During a round of intensive questioning, Davis refuted a suggestion that the government was "winging it" over Brexit. "The prime minister is absolutely clear: we are leaving the customs union and will be free to strike our own trade deals around the world", he said.
The government has said it needs the powers to be able to meet a tight deadline to effectively "copy and paste" European Union rules and regulations into British law by the time of Brexit.
"We have been clear that this is a vote either to accept the deal or reject it", said the PM's spokesman.