Why is everyone in the Labour Party so relaxed about the Brexit talks? The opposition is badly split about how best to respond to the United Kingdom’s 2016 vote to leave the European Union: for some it is a disaster, for others it is a crowning triumph. There are shadow ministers who think that frustrating Brexit will finish off the Labour Party – and shadow ministers who think facilitating it will do the same. There are backbenchers who think they will lose their jobs if we leave the EU, and there are backbenchers who think they will lose their jobs if we don’t.

The division is present in every one of the party’s tribes and factions, from the soft left to the old right. It is sufficiently acrimonious that Labour MPs who have been allies for decades have stopped speaking to one another because of it.

Yet when you ask Labour MPs about the negotiations between the party leadership and the government to resolve the deadlock, almost everyone is intensely relaxed, no matter what their preferred outcome is. The shadow cabinet hasn’t split into new tribes: there is no one quietly plotting a way to facilitate or to wreck the talks. Why not?

Labour’s pro-Europeans take their cue from the party’s shadow Brexit secretary, Keir Starmer, and his aides. Although Starmer is not universally popular with this faction, he is respected as their man on the inside. And here’s what they take from his account of the talks: although Jeremy Corbyn and Theresa May have met to discuss the impasse, the bulk of the discussions have taken place at a ministerial level. Facing Starmer across the table is May’s de facto deputy David Lidington.

Lidington is well-liked and his conduct has been widely praised by opposition MPs who have met him, but the impression they have conveyed to colleagues is of a man who does not have the political freedom to make them a genuine offer.

One of those familiar with the talks likened the Conservative approach to the puzzle books Where’s Wally? There is a repeated insistence that Labour will find a Brexit deal it can sign up to – if it simply looks hard enough at the deal that Theresa May has already negotiated. Now, some in Labour, both on the back benches and in the shadow cabinet, think that is true. But they also believe that supporting the Brexit deal without a significant concession – or, at least, a concession that looks significant – is to court political oblivion.

This line of thinking leads to a new deadlock. The talks will not progress unless Lidington can make a big offer that allows Corbyn to declare victory. Yet any offer big enough to fulfil that criterion would cause explosions on the Tory side. So the matter won’t arise. And if the Conservatives try to agree a deal without a “confirmatory referendum”, there are plenty of Labour votes to sink that plan on the floor of the Commons.

What about the other side? Labour MPs who fear a referendum rerun, or a dangerously soft Brexit, also believe they have someone on the inside: Rebecca Long-Bailey, the shadow business and industrial strategy secretary, and protégée of John McDonnell. They also believe that Jeremy Corbyn’s long-standing Euroscepticism, and the Euroscepticism of many of his closest allies, means he will never sign off a deal that could overturn the 2016 referendum result.

Are they right? Quite probably, but not for the reasons they think. No one who knows the Labour leader well privately disputes that he remains a Eurosceptic. Among his inner circle, traditional left-wing Euroscepticism, with its accompanying distrust for the European Court of Justice, is rife.

Corbyn’s strategy chief, Seumas Milne, is a hate figure among pro-Europeans inside and outside parliament. Corbyn relies on Milne heavily – in meetings with the other opposition parties, the Labour leader tends to give a brief preamble and to leave the detail to his aide – but that is irrelevant here. Milne is not wielding sinister influence over Corbyn on the Europe question: the two men agree entirely.

They have also both shown a willingness to compromise. The shape of Brexit that Corbyn has said he will accept already falls far from the left Euroscepticism dream by retaining a substantial role for the EU’s rule-setting organisations. Labour’s chief negotiating ask – to remain in a customs union – would also mean continued participation in EU-wide trade negotiations and arbitration panels.

The “M” that really matters as far as Labour’s Brexit strategy is not Milne but Mansfield: the ex-industrial Leave-voting English constituency that went blue last time. The recapture of marginals such as Mansfield is the dominant strategic objective of the Labour leadership. It is towns such as this that have shaped the Labour leadership’s Brexit approach, rather than a long-term commitment to quitting the bloc. That means the Labour MPs who want Brexit settled – largely because of electoral calculations, rather than ideological ones – aren’t worried about the outcome of the Brexit talks either. Corbyn won’t sign up to rerunning the 2016 vote, they reckon, because that will upset the voters of Mansfield. And so a strange equilibrium persists.

Labour MPs who want to stop Brexit and those who want to facilitate it believe that inaction serves their interests. Both sides hoped that the local election results would discredit their internal opponents. But while Labour did poorly in heavily pro-Leave areas, the biggest winners in terms of overall seats were the Greens and the Liberal Democrats – two anti-Brexit parties. So neither side can claim a decisive victory.

Both sides of the Labour split believe that something will happen to make sure their preferred outcome takes place, without them having to act directly. One of them is going to end up disappointed.