What is Labour's actual position on the Irish backstop? That's the question raised by a round of broadcast interviews given by Jeremy Corbyn in the wake of his Brexit talks with Theresa May this afternoon.

Corbyn told both Sky and the BBC that he had told the prime minister it was unacceptable that the UK could not quit the arrangement - designed to keep the Irish border open in the absence of a trade deal that does so - unilaterally, as he has repeatedly over the last few months. That much isn't new.

But his continuing insistence on changes to the backstop is nonetheless confused and confusing. Unlike the government, Labour whipped against Graham Brady's amendment demanding changes to the backstop last night, and Corbyn himself told the prime minister that changes to the backstop would not solve the parliamentary impasse earlier today.

He is right - which is precisely why his emphasis on the backstop makes such little sense. If Labour is to vote for a Brexit deal, it will be one that includes a permanent customs union or something effectively identical to it, as well as a high level of regulatory alignment.

Both the Labour leadership and the European Commission have said such a deal would obviate the need for the all-UK customs union element of the backstop. The regulatory bolt-ons that apply to Northern Ireland only are slightly more complicated but it would not take a massive leap from Labour's current position on the single market to ensure that element of the backstop wasn't triggered either.

Indeed, until recently, Corbyn's spokesman was wont to insist that Labour's commitments on the shape of the future trade relationship meant that it probably wouldn't need to agree to a withdrawal agreement with a backstop at all. That isn't quite true. But it's fair to say that the chances of the UK falling into it would be considerably smaller if parliament passed a Brexit deal that was acceptable to the Labour leadership.

Even in the event that its provisions did kick in indefinitely, it would effectively provide the permanent customs union that Labour accepts is necessary in order to maintain an open border and protect the Good Friday Agreement. So Corbyn's continued agitation for a unilateral exit clause makes very little sense on its own terms, especially given his opposition to the Brady amendment.

It is politically myopic too. It contradicts Labour's own policy, which mandates that any backstop must be acceptable to both communities in Northern Ireland (unlike the DUP and UUP, the main parties of nationalism and the non-sectarian Alliance support the backstop as is).

It is also causing serious consternation among his own MPs - some of whom have repeatedly made their concerns clear to Keir Starmer and Tony Lloyd, the shadow Northern Ireland secretary (Conor McGinn, the Newry-born MP for St Helens North, says he is "disappointed" by Corbyn's comments and urges him to back the Good Friday Agreement). It is fraying Labour's bonds with its sister party, the SDLP, and this stuff goes down very badly in Dublin too. Nothing assures the Irish government that its refusal to budge and take the promises on their word is justified more than statements like Corbyn's.

The time that Labour might have been able to drive a wedge between the Tories and DUP with this sort of rhetoric for political gain has long passed. All it does is erode the party's reputation for responsibility as far as the peace process is concerned. Labour MPs often argue that this Tory Brexit is jeopardising Northern Ireland's stability. The uncomfortable truth is that plenty of people are saying the same about what the debate over the backstop has done to their leader.