When boxers go into a clinch it looks more like a tender embrace than a fight. The same is true of the clash between Labour and the Tories. There is no affection between England’s heavyweight parties, but there is a kind of intimacy about the way they lean into their antagonism for tactical comfort.

Boris Johnson is glad to have Jeremy Corbyn to campaign against, and the feeling is mutual. Fear of installing a radical socialist in Downing Street imposes discipline on Tory ranks, while the Conservative leader presents Labour with a caricature of its arch enemy – careless, heartless and posh.

Both sides like politics that is binary and polarised. Traditional allegiances have been melting in the Brexit crucible, but whatever shape a constitutional crisis this autumn takes, it will culminate in the question of who should be prime minister. Corbyn and Johnson calculate that the smaller players – Liberal Democrats, the Brexit party, Scottish and Welsh nationalists, Greens, independents – will then be forced to line up behind either the Labour or Tory leader.

Johnson is doing the better job of consolidating his side, poaching back supporters of Nigel Farage by promising them everything they want. Corbyn has a fussier message, opposing a no-deal Brexit without rejecting the ambition to leave the EU. That drives remainers towards parties with less convoluted pro-European positions.

There is polling evidence that voters’ political identities are anchored more firmly on a remain-leave axis than traditional distinctions of left and right. It is less clear whether that realignment is robust enough to overcome an electoral system that – in England, at least – funnels votes into the usual blue and red buckets.

The Lib Dem victory in the Brecon and Radnorshire byelection, achieved by the Green and Plaid Cymru candidates’ withdrawal from the race, showed how it might be done. It was the prototype for a remain alliance general election ticket. Talks are under way to establish which seats might be nobbled with the same method and – trickier to negotiate – who should step aside for whom. That discussion is easily bogged down in local rivalries and historical vendettas. The Greens are wary, having put similar efforts into a “progressive alliance” in 2017 and come away feeling that their cooperative spirit was not properly reciprocated by the Lib Dems. The lingering smell of coalition with the Tories also deters leftwing Green members from embracing Jo Swinson’s party. There are petty tribalists on all sides who see prospective allies as chiselers or cranks.

But Brexit is a powerful motivator. It helps that the Electoral Commission has approved use of a “Unite to Remain” label on ballot papers, alongside a party name. That eases the taboo for activists campaigning for candidates they are used to treating as rivals. The Unite to Remain umbrella also brings financial assistance from pro-European donors. Most ambitiously, there is tentative discussion of a common platform reaching beyond the European question. One model is a four-point agenda that, alongside a referendum, would include investment in public services (styled as an anti-austerity dividend made available by the cancellation of Brexit), electoral reform and ambitious de-carbonisation targets.

The choreography is not simple. No party wants to look as if it is being led in the dance by a dominant partner. But it is heartening that committed pro-Europeans are thinking about coordinating policy steps when Tory campaign theme music – tough on crime, munificent with the NHS – is blaring out of every Downing Street window.

Facebook Twitter Pinterest ‘Since Corbyn does not identify himself as a remainer, his diehard supporters are obliged to see remain itself as a suspicious category.’ Photograph: Aaron Chown/PA

Even if there is not a ballot in the autumn, it is good exercise for pro-European politicians to develop the muscles for climbing between political trenches. Voter aversion to Corbyn and Johnson has been fostered by Brexit, but is not limited to it. There is a cultural appetite for alternatives that will outlast any resolution to the EU question. The electoral territory of Remainia might refuse to be partitioned back into Labour and Tory possessions.

That is Swinson’s hope and the reason she bluntly rejects any notion of supporting a Corbyn-led government. Disgruntled Labour pro-Europeans have fuelled the Lib Dem renaissance so far, but when it comes to Westminster seats, a breakthrough must include liberal-minded Tories who are equally appalled by the Trumpian fever that has gripped the government and chilled by hard left fervour in Labour. Swinson also wants to persuade independent MPs in the Commons to follow Chuka Umunna’s example and rebadge as Lib Dems. She can’t attract refugees from Corbynism while flirting with support for a pro-Corbyn coalition somewhere down the line.

For Labour, the Lib Dems have always been a contemptible nuisance: plastic progressives; squatters who make it harder to evict Tories from office. The remain alliance will be viewed the same way and attacked as enablers of conservatism. Some hostility is rational given that the project’s purpose is to rival Labour for the status of principal national opposition. But giving venomous expression to that enmity is counterproductive. There is a strain of piety on the left that refuses to believe in valid political expressions of compassion that are not Labour-branded.

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Since Corbyn does not identify himself as a remainer, his diehard supporters are obliged to see remain itself as a suspicious category – a tactical diversion by soulless centrists who cannot be sincerely worried about inequality or distressed by austerity because if they were they would surely be supporting Labour.

Bolstered by that moral arrogance, the official opposition party expects – nay, demands – that pro-Europeans do their duty and get behind the Labour leader as the only feasible candidate to replace a wicked Tory. That is the way British politics has worked for the best part of a century. But Brexit has the makings of a 100-year storm. And while it is fanciful to imagine a remain alliance breaking the mould in a matter of weeks, believing it might be possible will give hope to a lot of voters. Because the alternative is watching Johnson and Corbyn slug it out, wishing they could somehow both lose.

• Rafael Behr is a Guardian columnist