Theresa May is battling to avert a rebellion inside her own party amid fears of euroskeptic Tories that she will break her promise to take the United Kingdom out of the European Union's trade regime.
Ten Tory MPs are expected to vote in favour of a customs union, overturning May's majority.
"It is coming from the pro-Brexit section of the party and it's deeply unhelpful".
Though the looming Commons vote on a pro-customs union motion would be a symbolic, non-binding one, it has the potential to deepen Tory wounds on Brexit.
Theresa May is preparing to surrender over her promise to leave the Customs Union with senior advisers to the prime minister telling the Sunday Times that she is now willing to live with a Commons defeat on the issue.
Theresa May will remain committed to leaving the customs union, despite a defeat in the House of Lords over the issue and rumours that her position may be softening. Such deals can't be reached while the U.K.is covered by European Union bilateral accords.
"We need to make it absolutely clear that leaving the customs union is an absolutely fundamental part of Brexit".
But there are growing concerns about the impact of cutting ties with Britain's largest trading partner, and the possible risk to peace in Northern Ireland by introducing an Irish border in the event of a "hard" Brexit.
"If they want my support for the final deal they can't move away from the prime minister's '[Mansion House] speech", Bridgen said.
The main topic will be discussion of the U.K.'s aims for worldwide trade after Brexit, according to the official, and will nearly certainly involve consideration of the customs deal the country will seek to reach with the bloc.
"The only thing that will save her now is if she makes clear that there will be no more backsliding", one member of the anti-EU grouping the European Research Group led by Jacob Rees-Mogg told Business Insider earlier this year.
However, it would also be hugely controversial with senior members of the Cabinet, with Downing Street now believing that the International Trade Secretary Liam Fox and the Foreign Secretary Boris Johnson could both resign.
United Kingdom media (including the Guardian, Independent and Times) are reporting that May could face a cabinet revolt over her comments affirming that they would leave the European Union trade arrangement and wouldn't join a similar one. The newspaper quoted one aide saying May would not be upset if Parliament forced her to stay in the customs framework by voting against her plans to leave it, though one person familiar with the prime minister's thinking disputed the account. Time is running out for negotiations to reach a deal on the terms of Brexit and a framework for the future trade agreement by October.