Senior Tory backbencher Peter Bone said the former minister’s amendment to the Trade Bill is a “fundamental” confidence issue in the Government which potentially opens the door to a hard-Left government under Jeremy Corbyn’s Labour Party.
Ms Soubry, the leading Remainer on the Tory backbenches, has teamed up with Labour MP Chuka Umunna to try to keep Britain in the EU Customs Union.
The policy looks set to be backed by Mr Corbyn in a speech he will be giving on Monday after a strong signal by shadow foreign secretary Emily Thornberry.
Ms Thornberry made it clear Labour wanted close ties to Brussels, telling LBC radio: “Technically, because we are leaving the European Union we can’t be in the Customs Union that we are in now. So, we leave and then we negotiate a new agreement.
“That, we think, is likely to be a Customs Union that will look pretty much like the current Customs Union.”
A significant rebellion by Tory Remainers would defeat Theresa May on a manifesto issue and key Brexit policy.
Mrs May has been clear she wants to leave the Customs Union. If the UK remains then Brussels will control British trade policy, making it impossible to make free trade agreements with the rest of the world.
Mr Bone, founder of the Brexit campaign group Grassroots Out, said: “The Government needs to start making it clear that votes like these are confidence issues.
“Conservative MPs need to understand that by rebelling they will bring down the Government and cause another general election.”
Ms Soubry, who has demanded Brexiteers are thrown out of the Conservative Party, has claimed she has widespread support for her amendment.
Other Tory MPs to sign Ms Soubry’s amendment are Remainer rebels Nicky Morgan, Stephen Hammond, Heidi Allen, Jonathan Djanogly and Sarah Wollaston.