The DUP has warned it will bring down Theresa May's Government if Northern Ireland is forced to stay in the Single Market or Customs Union after Brexit.
Nigel Dodds, the leader of the Democratic Unionist Party at Westminster, said his party would vote against the Government if any of its "red lines" on Brexit were crossed.
It comes as Britain and the EU are deadlocked over how to ensure that there is no hard border between Ireland and Northern Ireland after Brexit.
Mr Dodds told the Conservativehome website: “If, as a result of the Brexit negotiations for instance, there was to be any suggestion that Northern Ireland would be treated differently in a way, for instance that we were part of a customs union and a single market and the rest of the UK wasn’t ... for us that would be a red line, which we would vote against the Government.
“You might as well have a Corbyn government pursuing openly its anti-Unionist policies as have a Conservative Government doing it by a different means.”
It comes as Tory MPs will on Thursday hold a symbolic vote on keeping Britain in a customs union. Bob Neill, Nicky Morgan and Sarah Wollaston are among Tory MPs backing the motion, which urges the Government to “include as an objective in negotiations ... the establishment of an effective customs union”.
Ministers have said that the vote is "meaningless" because it is not binding. As a result Tory MPs will not be whipped into attending the vote.
David Davis, the Brexit Secretary, said he would have personally "failed" if the UK has to stay in a customs union after Brexit.
He also suggested that the EU was posturing when it last week ruled out Britain's solutions over the Irish border as he insisted Brussels was simply setting out "opening positions" for negotiations.
He told the Treasury select committee: “I do not expect the solution to be an extension of the Customs Union. I would view that on my part as a failure.”
Andrea Leadsom, the Leader of the Commons, told BBC Radio 5 Live: "With regards to being in a customs union, once you leave the European Union – if you stay in the Customs Union – you cannot negotiate your own free trade agreements.
"Genuinely, I cannot understand why anybody accepts leaving the EU but staying in the Customs Union. That's the worst of all worlds."
In the Commons Mrs May reiterated her pledge to take Britain out of the Customs Union.
She said: "The British people voted to leave the European Union, in voting to leave the European Union they voted to leave the Single Market and the Customs Union."
Mr Davis left open the possibility that Mrs May could be forced to return to Brussels to seek a new Brexit deal if MPs reject her original offer.
He admitted that a Commons resolution to approve the Brexit deal could be amended by MPs, amid concerns among Brexiteers that pro-European Tory MPs could join forces with Labour to keep Britain in the Customs Union.
Mr Davis told the Brexit select committee that the “meaningful vote” on a resolution to approve the Brexit deal could be amended. “If you can tell me how to write an unamendable motion, I will take a tutorial,” he said. It comes after Mrs May delayed a Cabinet debate over Britain's future relationship with the EU until next week.
The Prime Minister's Brexit war Cabinet met on Tuesday but did not discuss the Government's two options for a customs relationship with the EU after Brexit.
Boris Johnson, David Davis, Michael Gove and Liam Fox are opposed to plans for a customs partnership, which would involve Britain collecting tariffs from imports on behalf of the EU. They believe the plan is unworkable and could lead to the UK ultimately staying in the Customs Union, limiting its ability to strike a free trade deal.