Jeremy Corbyn does not have a better plan for Brexit than Theresa May but, so far, he hasn’t needed one. After the referendum, the prime minister and the Labour leader embarked on parallel journeys, each carrying promises of painless, cost-free release from EU membership. May’s path was harder. Her pledges were snagged on governing reality, skewered by Brussels, hung up on parliamentary arithmetic. Opposition has protected Corbyn from those jagged edges, but he cannot avoid them for ever. Rebellion in the House of Lords has brought them uncomfortably close.

The upper chamber has rewritten the EU withdrawal bill so it urges the government to negotiate a much softer Brexit. More than 80 Labour peers defied their whips to support membership of the European Economic Area, thereby preserving British integration in the single market. There are MPs from all parties who will want to endorse that amendment when it comes back to the Commons. They see the EEA as the least-damaging Brexit model: a safety net for jobs and investment.

At a factory in Essex today, three political grandees gathered to make that argument: David Miliband, former Labour foreign secretary; Nick Clegg, former Liberal Democrat leader; and Nicky Morgan, Tory chair of the Treasury select committee. The intended symbolism of the triptych was that averting a hard Brexit is a mission that transcends party boundaries.

That message might resonate with some non-aligned voters, but it is hard to imagine a collection of messengers less likely to shift opinion in Corbyn’s camp. The official Labour view is that single market membership is incompatible with the referendum result. That is a facsimile of May’s argument. It is also untrue. The ballot paper had no subsidiary questions on post-EU arrangements. So why is Labour pumping up the tyres on May’s hard Brexit bus?

Miliband, Clegg and Morgan: it’s difficult to imagine a group of messengers less likely to shift opinion in his camp

Three reasons stand out. First: a fear of being cast as Europhile saboteurs. In legal terms, the EEA is not the European Union, but in cultural terms the accusation of a sellout resonates with many leave voters. Labour is not polling well enough in areas that voted for Brexit to risk letting off a remain-themed firework in parliament.

Second: squeamishness about immigration policy – EEA membership would preserve free labour movement. That doesn’t have to mean totally unregulated borders: there are mechanisms such as work permits for managing migration from within the single market. But to advertise them, Labour would have to take the initiative on a subject that is fraught with risk. Perceived softness on immigration costs the party votes, while any hardening of rhetoric would jar with Corbyn’s caring brand. By rejecting the single market he can be strict on borders without sounding mean to foreigners.

Third: there is ideological hostility to single market rules prohibiting certain forms of industrial subsidy. Those restrictions, it is argued, would obstruct a radical-left economic programme. Whether that is true depends on how radical and how left you want to go. Everything in Corbyn’s 2017 manifesto could have been implemented within existing EU rules. The leader’s office might be fizzing with more drastic anti-capitalist plans, but no one says what they are.

The arguments over Labour’s Brexit position are a tangle of dogma, idealism and electoral pragmatism. They don’t map neatly on to the outdated scheme of a Corbynite movement in conflict with a Blairite reaction. There are Momentum activists who burn with the spirit of remain. There are Labour MPs who would bury Corbynism but also bow to the Eurosceptic will of their constituents.

The more fundamental distinction is between those who start from the belief that any Labour government is always better than any alternative, and those who don’t. For tribal loyalists, Brexit strategy is subordinate to the goal of beating the Tories. That is the lens the leadership applies and it would be bizarre if it didn’t. (Whether it makes the right choices to achieve that goal is a different matter.)

Then there is the ethos expressed by Miliband, Clegg and Morgan today, that getting Brexit right is in the national interest, bigger than any party. There are Labour backbenchers who have no affection for the current leadership but cannot imagine campaigning in a rosette that isn’t red. But others have crossed that psychological Rubicon. They expect to be driven out of the party before a general election, either by the Corbyn machine or their own consciences. Their allegiance is more remain than Labour. They will vote accordingly.

Beyond parliament, tension between pro-European and pro-Labour feelings is strangely submerged. Many of Corbyn’s enthusiastic younger fans are also eager remainers. The leadership strategy seems to be to persuade them that leaving the EU is only a disaster because it is being organised by Tories. Make Jeremy prime minister, the argument goes, and the bad feelings disappear. It is true Corbyn commands phenomenal amounts of trust. But many of his supporters also want to stop Brexit, or at least to vote on it again. And they can see that their leader is less bothered.

Corbyn’s eager acceptance of the referendum result could, at first, be lauded as fulfilling his duty as a democrat. The same could just about be said when he voted for article 50 and again when he ran on a pro-Brexit manifesto. When he sacked a shadow cabinet minister who called for another referendum, it was a question of loyalty and discipline … But then, why doesn’t Corbyn want a public vote on the final deal? Why would he whip MPs to abstain in a vote to make Brexit softer? Why take the afternoon off to make a Tory prime minister’s job easier?

At some point even the most indulgent audience will see these as the choices of a leader who not only likes Brexit, but likes it hard. Then the question is whether Labour remainers trust Corbyn more than they hate leaving the EU. How far can he test their patience? He seems determined to find out.

• Rafael Behr is a Guardian columnist