Theresa May will get an idea of how much opposition there is to a key plank of her Brexit plan as MPs debate the decision to leave the EU customs union.
It comes after ministers were defeated on the issue in the House of Lords and ahead of key votes for MPs next month.
The PM has ruled out joining a customs union, but Labour, the Lib Dems and the SNP, plus a handful of Tories, are in favour of having one in some form.
Downing Street called it a "routine backbench business debate".
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Mrs May is under pressure from both sides of the EU debate on the issue of the customs union, which allows for goods to be transported tariff-free between EU member states.
Brexiteers have criticised a suggested "customs partnership" arrangement to replace the current arrangements, while pro-EU campaigners say a customs union is the only way to prevent a hard border in Northern Ireland.
It is not clear whether there will be a vote at the end of Thursday's debate, but crunch votes are expected in the coming weeks when Remain-supporting MPs will push for a change of course.
The motion being debated on Thursday calls on the government to include as an objective in negotiations with the EU "the establishment of an effective customs union between the two territories".
Signatories to the non-binding motion include four senior Tories: Bob Neill, Sarah Wollaston, Nicky Morgan and Dominic Grieve.
Yvette Cooper, who chairs the Home Affairs Committee, and Treasury select committee chairwoman Ms Morgan said in a joint statement: "We both believe the case for a customs union is overwhelming – for the sake of British manufacturing, international trade, smooth borders and Northern Ireland peace."
What is a customs union?
A customs union is when countries agree to apply the same taxes on imports to goods from outside the union.
This means when goods have cleared customs in one country, they can be shipped to others in the union without further tariffs being imposed.
If the UK remains part of the customs union, it would be unable to strike trade deals with countries around the world, but supporters say it would help keep an open border between Ireland and Northern Ireland.
On Wednesday, Brexit Secretary David Davis told the Brexit Select Committee he expects Parliament to "uphold" the government's policy of leaving the customs union.
Shadow Brexit secretary Keir Starmer accused the prime minister of delaying a Commons vote on the issue "for fear of a defeat".
"In light of the government's own impact assessments and the lack of progress on any new trade deals, any economic case for ruling out a customs union has collapsed," he said.
"The prime minister is now solely focused on internal party management and masking the divisions within her government."
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But Brexit minister Suella Braverman said Labour's support for a customs union "would leave the UK shackled to Brussels", meaning the UK would be unable to make trade deals.
Labour leader Jeremy Corbyn has backed a customs union, but only if the UK had a say in future EU trade deals.
Mrs Braverman said: "The supposed safeguards that Corbyn talks about are impossible to achieve."
Labour was "more interested in frustrating the process and playing politics than they are in delivering a successful Brexit", she said.
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Your guide to Brexit jargon
Mrs May has ruled out joining a customs union but has come up with two options to avoid a hard border in Ireland.
One of them is a "customs partnership" that would involve the UK collecting the EU's tariffs on goods coming from other countries on the EU's behalf.
If those goods didn't leave the UK and UK tariffs were lower, companies could then claim back the difference.
This option has been heavily criticised by some Brexiteers, with influential backbench Tory MP Jacob Rees-Mogg branding it "completely cretinous".
The other option being proposed by the government would be to minimise checks rather than getting rid of them altogether, by using new technologies and putting in place a trusted trader scheme.