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.