MPs will hold a non-binding vote on the issue on Thursday after the Lords voted for some form of future customs union. Such a move could trigger a challenge to May's leadership from Brexit campaigners in the Conservative Party.
While numerous defeats were expected, it is the rifts over whether to remain in a customs union with the EU that have taken centre stage.
The question of whether to leave the customs union goes to the heart of the kind of Brexit the United Kingdom will get.
Mr Davis said the best solution from a British perspective was a comprehensive free trade agreement combined with a deal to recognise shared regulations and customs procedures.
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'But I also recognise the importance to businesses like this of being able to have as frictionless a border as possible into the European Union'. European officials also see staying in the arrangement as a potential solution to the otherwise intractable issue of how to avoid a hard border between the United Kingdom and Ireland after Brexit.
Brexit minister David Davis said today that he believed that there was a high probability that Britain would negotiate a deal to leave the European Union.
Mr Davis dismissed suggestions that the government's own modelling showed the potential from future trade deals did not outweigh the benefits of being in the EU.
David Davis, Liam Fox and Boris Johnson are to press the Prime Minister to abandon any softening of her stance which emerged following reports last week that Brussels rejected the UK's Irish border plans.
She could lose her job and be replaced by a Brexiteer like Jacob Rees Mogg.
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The battle over customs rules is likely to reach a climax in a Commons vote as early as next month. The legislature is additionally confronting parliamentary conquer on an open deliberation over the issue one week from now.
If Britain remains in a customs union with the EU, it would make commerce with the bloc easier.
A spokesman for the prime minister said statements made by European Union chief negotiator Michel Barnier represented an "inevitable public comment" before a new round of talks began, stressing that Prime Minister Theresa May would focus on discussions at the negotiating table. The Times reported in Monday's edition that May favors a close partnership deal in which the United Kingdom conducts the EU's customs checks on the bloc's behalf, but that some of her ministers believe this won't work.
Supporters of staying in the customs union argue that it is the safest option for the economy as it will allow goods and trade to continue to flow without barriers when Britain leaves the EU.
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