The Conservative party's inability to agree on the EU Withdrawal Bill might cause the downfall of Theresa May

This week the EU Withdrawal Bill returns to the House of Commons, with government sources insisting that all talk of a U-turn over Britain’s departure from the EU’s customs union is misplaced.

After defeat on the issue in the Lords last week, pro-Remain Tory rebels claimed to have been told that attempts to follow suit in the lower house – notably when MPs get a meaningful vote on the subject as early as next month – would not be turned into a question of confidence in the prime minister. Hardened Brexiteers, meanwhile, have briefed journalists that such an attempt would indeed be regarded by No 10 as a vote against Theresa May’s position.

The Conservatives, not for the first time over Europe, are in a muddle. Labour, on the other hand, is finding unity in the face of the government’s fractures.

As things stand, the government maintains that Britain will certainly leave the customs union when it leaves the EU – and that to do otherwise would amount to a betrayal of the referendum result. Its alternative proposal is to develop a new approach that somehow, by means as yet unclear, avoids customs checks at UK-EU borders but enables Britain to strike its own trade details with other countries.

The lack of detail accompanying the proposal is indicative of the broader uncertainty over how Brexit is likely to play out. It is also reasonable to surmise that the need to resolve the Irish border question is as integral to this vague plan as the need to replace the existing customs union with a sensible trade deal per se.

Ministers may like to believe that technology will make all things possible but the simple truth is that the government is nowhere near to having offered a convincing explanation of how its scheme would work in practice. No wonder that EU figures regard the idea as something approaching fantasy. And no wonder too that critics in both houses of parliament are seemingly willing to give the government a bloody nose on the issue.

Labour, it should be said, is hardly offering much clarity of its own, arguing simply that it would – were it in government – take Britain out of the present customs union and negotiate a new one that would have the same effects. It has the advantage, however, of not running the country. All the pressure is on the Conservatives.

A vote this week on the question will be non-binding and was dismissed by former minister John Whittingdale as “a piece of theatre”. But the more time that passes, and the more that Remainer voices take centre stage, the more the government’s position becomes exposed.

The possibility of Theresa May finding herself boxed into a nightmare confidence vote next month is not one that can be easily dismissed, therefore. Nor would it be a positive result for the prime minister it to be a foregone conclusion, given the government’s precarious position in the house.

At the weekend, justice secretary David Gauke told the BBC that he believed the government could persuade sceptics in parliament of the case for leaving the customs union “but ensuring that we don’t put in place unnecessary barriers to our trade with the EU”.

As a matter of principle Mr Gauke may be correct. Yet the government’s problem is that it is offering inadequate information as to how that can be achieved. And while most would be prepared to accept that a solution is not likely to prove easy, the ongoing lack of detail only bolsters the suspicion that in fact, it is completely impossible.

From the very beginning of the Brexit negotiations, attempts to square the Irish border-customs union circle have appeared doomed. If rebels such as Ken Clarke decide to take the government on when it comes to a binding vote next month, it may be the issue that leaves Theresa May sunk.