It is easy to locate common ground between Theresa May and Jeremy Corbyn on Brexit. The terrain has been mapped. The prime minister and the Labour leader both claim to want to take the UK out of the EU, and there is a document describing in great detail how it would be done. It is not a secret text. You can download it from the government website. It is the withdrawal agreement that May negotiated last year. No other legal method for enacting Brexit exists, nor is any alternative blueprint going to be drafted. If Corbyn were to win a general election pledging a softer, rosier Brexit, the subsequent talks in Brussels would begin with him accepting conditions agreed by his predecessor.

There is still the long-term character of the UK’s relationship with its neighbours to be settled, which is why Labour MPs who support Brexit voted to stop it happening under a Tory prime minister. They can’t trust the Conservative party to make good choices about Britain’s future inside or outside the EU. But that reservation sows dishonesty into the cross-party talks that resumed in Downing Street yesterday. There is nothing left to discuss on the withdrawal agreement. The options are May’s version or nothing. And anything more ambitious involves Labour and Tory frontbenches joining forces to legislate on the broad outline of a European strategy. It means May and Corbyn whipping their MPs into the same voting lobby, defending the same positions, defending each other. That isn’t going to happen.

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Neither leader has the temperament, imagination or backbench support to make that work. They are also at different stages in their political life cycles. For May, Brexit is a legacy issue. She has been forced to surrender any hope of doing anything else in politics. For Corbyn, Brexit is something to get out of the way before the real work begins. It is a distraction and a nuisance, hogging the stage to the exclusion of eye-catching leftwing policies.

This would be less of a problem if the subject could really be changed by nudging some rebranded variant of May’s deal over the line. It can’t. In every Brexit model, the UK gets locked in a Brussels antechamber, pressing an ear to the door where the big continental decisions are being made. Any prime minister who governs Britain outside the EU will be constantly cursing that arrangement. No candidate to replace May wants to be cited as a co-sponsor of her deal.

There is no appeal for Corbyn in reaching No 10 only to serve as a technocrat prime minister grinding through ever harder stages of Brexit. In that scenario, he is also besieged by a rabid nationalist opposition – some hybrid of a fanatically radicalised Tory party and Nigel Farage’s new Brexit party – bellowing that the dream of liberation has been traduced by a Labour party stuffed with unrepentant remainers.

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But Corbyn also doesn’t want to lead a charge against Brexit. He has no natural affection for a European project that was conceived on the capitalist, western side of the cold war frontline. That instinct is given strategic reinforcement by Labour MPs who see it as their electoral and democratic duty to satisfy the Eurosceptic demands of voters in areas that backed Brexit in 2016.

The evidence tells a more complicated story. Swings to the Liberal Democrats in last week’s council elections suggest that Labour support in leave areas depends heavily on the local remainer community. The difficulty in those heartland seats is not simply a matter of otherwise loyal voters withholding support because they want Corbyn to back Brexit. The corrosion of allegiance is deep-rooted and cultural, and it began before the referendum. Much of the damage pre-dates the Corbyn era, but some of it was inflicted in 2015, when the newly chosen leader was best known for backing unilateral disarmament and staying tight-lipped through the national anthem.

Corbyn’s supporters have always believed in his power to overcome those reservations with an armoury of popular policy and an evangelical pitch (as long as he is given a fair hearing). The 2017 general election briefly appeared to vindicate that view, but then the triumphal march stalled. Or rather, it was pushed aside by a different marching band whose tempo was dictated by Tory hardliners.

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No one now doubts that there is appetite in Britain for drastic upheaval, for ripping up the status quo. There is clearly political mileage in denouncing the establishment and scaring the bejesus out of bourgeois liberals. But the ideological engine of this insurgency turns out not to be the one that the Corbyn movement had in mind. That poses a dilemma. Should they co-opt the Brexit revolution or shut it down? Saddle and ride a nationalist tiger, or shoot it?

Having rejected a no-deal Brexit, Labour’s choices are restricted to a miserable compromise or a slide back towards full EU membership. Neither option has the ring of bold adventure that Corbynism once promised. Socialism deferred until the pesky European question has been resolved is not much of a rallying cry. Meanwhile, the radical right is on the rampage and Labour MPs seem confused as to whether they are defending moderation or opening a new front against it from the left.

And Corbyn himself comes across as impatient and frustrated with Brexit, but not in a way that speaks to the hearts of remainers or leavers. It is not an itch to complete the job or to abort it. Instead, the Labour leader sits tutting and drumming his fingers like a man who feels the wrong revolution has barged into history’s queue when it was meant to be his turn.

• Rafael Behr is a Guardian columnist