THERESA May is facing the prospect of a humiliating Commons defeat later today after Labour made clear it would support a rebel Conservative amendment to keep Britain in a customs union with the European Union.

A defeat on the flagship Trade Bill would throw the Prime Minister’s controversial Chequers Plan into disarray because at its heart is the contention that Britain will not be part of a customs union because such a move would prevent it from agreeing trade deals post-Brexit.

On Tuesday there was high drama at Westminster when the UK Government “caved in” to Brexiteer demands on the issue of supporting a plan to have a reciprocal arrangement with the EU on the collection of tariffs; something Brussels is unlikely to agree to.

The volteface angered Remainer Tories, who opposed the Government in the vote; one minister, Guto Bebb, resigned so he could vote against the newly amended bill; making him the 10th person to resign over Brexit.

The Government won the vote but only just; by just three votes.

Alistair Carmichael, the Liberal Democrat chief whip, accepted responsibility, saying he had “messed up” after the party leader, Sir Vince Cable, and his predecessor, Tim Farron, both failed to turn up to vote. Jo Swinson, the deputy leader also did not vote but she is on maternity leave. Mr Farron later apologised.

As Julian Smith, the Conservative chief whip, and his Government colleagues make a last-ditch bid to avert a humiliating defeat this evening, Labour made clear it would support an amendment tabled by Tory remainers Nicky Morgan and Stephen Hammond, which would mean the UK would join a customs union with the EU if no agreement were reached on frictionless trade by January 21 2019.

Ahead of the regular weekly Cabinet in Downing St, Mrs May held a political Cabinet of senior party colleagues to map out a strategy for the day. She was due to have talks with association chairmen and women; perhaps an indication that pressure will be piled on wavering Tory MPs.

Yet pro-EU Conservatives believe they have as many as 10 colleagues, who will be willing to support the customs union amendment, including possibly a couple of ministers.

A senior Labour source also made clear it would have Opposition support.

He explained: “We saw yesterday there is no majority for May’s Chequers’ agreement. But there is a majority for a customs union. Today parliament has the chance to change the course of the Brexit negotiations, protect jobs and the economy. Fingers crossed, the Lib Dems turn up.”

The Liberal Democrats and the SNP are expected to back the rebel Tory amendment, placing the vote on a knife-edge.

Earlier, Liam Fox, the International Trade Secretary, insisted the Chequers compromise on Brexit was not dead as some had suggested.

He told BBC Radio 4's Today programme: "The wording of the amendment yesterday was very close to the wording in the Government's White Paper. It looked in fact as a bit of a cut and paste from the White Paper."

The Scot said he wanted to see a "people's Brexit", stating: "We can't please everybody; we have to have a compromise position that enables the country to get an agreement with the European Union.

"Here in Britain there is far too much negative, self-doubting pessimism in this process," he added.

Dr Fox’s Tory colleague, the pro-EU Heidi Allen, suggested she and other Remain supporters had been prepared to drop their own proposed amendments to the Chequers Plan on the customs union before "extreme last-minute manoeuvres from the[pro-Brexit] European Research Group[headed by Jacob Rees-Mogg]".

"What was agreed at Chequers wasn't perfect to us, wasn't perfect to Leavers either, but the PM has worked exceptionally hard to find a decent first pitch to put the EU and to move forward from that.

"We were all set to drop all our amendments and back it and then suddenly we had these rather extreme last-minute manoeuvres from the ERG, which seemed to us to deviate the Prime Minister from her plan and we weren't prepared to let them do that; or at least try," added the MP for South Cambridgeshire.