Liam Fox has admitted the government may have to rely on Labour MPs to to push through its Brexit plan.
The international trade secretary also hinted he would quit the cabinet should Theresa May decide to u-turn and keep the UK in a customs union.
“I don’t think there is a customs union that could ever be acceptable,” he told BBC Radio 4′s Today programme on Tuesday.
“If we are in a customs union of any sort we will have less ability to shape Britain’s future than we have today. That is not what the public voted for.”
Last night May suffered her most damaging Brexit defeat so far after the House of Lords voted to give Parliament a say over the terms of any future EU deal.
Peers have also amended the EU (Withdrawal) Bill to order the government to keep open the option of staying in a customs union.
The prime minister faces a showdown with MPs when the legislation returns to the Commons.
If enough pro-Remain Tory MPs decide to defy the prime minister - she could lose the vote.
Fox said today. “We don’t have a parliamentary majority that’s for sure, that makes life harder.
“There are of course quite a number of Labour MPs who represent seats where there was a heavy vote in favor of leaving the EU who I would think were rash, to say the least, if they tried to openly confront the democratic view of their own voters.”
Asked if he would resign as trade secretary if May conceded ground and kept the UK in a customs union, Fox refused to rule it out.
“As you well know we don’t answer questions [on resignations],” he said. “It’s supposition.”
Fox also hit out at the Lords for attempting to “thwart” the “view of the British electorate in a referendum” and “legislation coming from the House of Commons”
This morning HuffPost UK learned one of Jeremy Corbyn’s frontbenchers has been “bollocked” but not sacked after he voted for a fresh referendum on Brexit.