Two Conservative MPs have defied their party line while Labour abstained on an amendment to the Government’s Brexit legislation which the Liberal Democrat’s claimed would have kept the door open to the single market.

While the amendment to the EU (Withdrawal) Bill was easily defeated – by 315 to 93 – it exposed divisions within Labour over its Brexit policy and the willingness of pro-EU Tories to vote against Theresa May’s instructions.

If the Lib Dem-led motion had passed, it would have prevented ministers from using regulation powers in the Withdrawal Bill to “create barriers” to the UK’s continued membership of the single market.

Division lists showed that two prominent Conservative MPs – the former Chancellor Ken Clarke and former minister Anna Soubry – voted for the motion, against the wishes of their party whip.

On Labour’s side, 44 MPs voted for the amendment despite the frontbench abstaining. The party would not confirm whether it ordered its MPs to abstain, simply adding they do not comment on whipping arrangements.

Shortly after the vote Vince Cable, the Liberal Democrat leader, accused the Labour party of “letting down” British workers.

“This ends any pretence that Jeremy Corbyn is fighting for us to stay in the single market,” he said. “He whipped his MPs to support the Conservatives, sitting on his hands rather than voting against their extreme Brexit plans.”

The Liberal Democrat MP Tom Brake, who put forward the amendment, said: “Labour whips telling Labour MPs to abstain on vote to stay in the single market. Sad. Their young supporters in particular will be disappointed. Pleased to see some Labour MPs disregarded their whip. Anna Soubry and Ken Clarke and the SNP also joined our ranks.”

The vote was just one of several during a late-night debate in the Commons on the Government’s Brexit legislation. A separate vote on an amendment to the legislation, requiring the Government to establish new domestic governance arrangements for environmental standards after Brexit, was also defeated by 315 votes to 293.

On another amendment, put forward by the Labour MP Yvette Cooper, aiming to place a general provision on the face of the Bill so that the delegated powers granted by the Bill should “be used only so far as necessary”. While this motion was also defeated, division lists showed that three Tory MPs rebelled, including Mr Clarke, Ms Soubry and former Education Secretary Nicky Morgan.

Brexit bonhomie as May finally seals agreement with EU leaders Show all 10 1 /10 Brexit bonhomie as May finally seals agreement with EU leaders Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May is welcomed by European Commission President Jean-Claude Juncker Reuters Brexit bonhomie as May finally seals agreement with EU leaders EU President Jean-Claude Juncker greeting Theresa May at the EU Commission in Brussels PA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May poses for a picture with European Council President Donald Tusk REUTERS Brexit bonhomie as May finally seals agreement with EU leaders EU Commission President Jean-Claude Juncker walks behind British Prime Minister Theresa May EPA Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May (L) and European Commission President Jean-Claude Juncker address a press conference at the European Commission in Brussels AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May speaks at a press conference with EU Commission President Jean-Claude Juncker EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union, David Davis (L) and Michel Barnier (2-L), the European Chief Negotiator of the Task Force for the Preparation and Conduct of the Negotiations with the United Kingdom under Article 50 enter the room by the emergency exit to attend British Prime Minister Theresa May press briefing on Brexit Negotiations in Brussels. EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union David Davis (L), Britain's Prime Minister Theresa May (2-L), European Commission President Jean-Claude Juncker (2-R) and European Union's chief Brexit negotiator Michel Barnier (R) in a meeting on Friday morning AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders European Union chief Brexit negotiator Michel Barnier speaks during a media conference at EU headquarters Brexit bonhomie as May finally seals agreement with EU leaders European Council President Donald Tusk addresses a media conference at the Europa building in Brussels AP

During the debate Ms Soubry, a pro-EU Conservative MP, also said ministers must “give a little bit more” to build a consensus with those who backed Remain during last year’s referendum. She said that if the Government is genuine in “healing the great divide” it should “reach out and do the right thing”.

Her comments came ahead of the seventh day of late-night debates and votes on the Government’s EU (Withdrawal) Bill – the legislation that aims to transpose EU law onto the UK statue book after Brexit.

Ms Soubry also criticised some of her colleagues for suggesting those who have tabled amendments to the legislation were seeking to “thwart” Brexit”, adding it is “gravely offensive” and said it must stop.

Speculation is rife that Downing Street could suffer its first defeat through an amendment on Wednesday over giving MPs a “meaningful vote” on any final Brexit deal.