Immigration is the stuck record of British politics, and Labour politics in particular. The issue has become to Labour what a trip to Stamford Bridge has to Arsenal: different tactics, different players, but the result – defeat – never changes.

When, shortly after Tony Blair’s third election victory, the Fabian Society began polling the voters who had left the party between the 2001 and 2005 elections, many expected that Iraq or tuition fees would loom large among the reasons given for giving up on Labour. Instead, immigration was the biggie.

That was the motor behind Gordon Brown’s “British jobs for British workers” riff shortly after he became Labour leader, behind Ed Miliband’s promise to “bear down” on immigration and those “controls on immigration” mugs. In its post-Blair, pre-Corbyn incarnation, Labour managed to locate the political equivalent of the “uncanny valley” – the point in which robots become lifelike enough to unnerve people but not enough to reassure them – appearing to be at once intensely relaxed about immigration to voters who wanted tougher border control and racist to those voters who thought that immigration was a good thing.

For most of its history, Labour has been able to rely on securing majorities of the vote from people who are in poverty and people who are concerned about poverty, usually enough to get around a third of the vote and around 250 seats in the House of Commons. The difficulty is that those two cores – both of which are essential to a Labour triumph – cannot agree over the immigration question.

As I’ve written before, the question of how the party reconciles its two cores may well be one beyond any politician, with potentially catastrophic consequences for Labour’s ability to govern again. Now Labour’s immigration problem has taken on epochal significance, thanks to its potential to send Britain crashing out of the European Union if enough of the party’s voters decide that greater control of Britain’s borders is worth the economic harm.

Regardless of the outcome, Labour has a devil of a time reconciling its two core votes – a subject on which MPs, commentators and think-tankers talk about “hard questions”, “addressing concerns”, “tough answers” but actually Labour’s problem comes down to one very easy question: are you for being part of the European Union, or not?

Outside of the European Union, Britain already has an “Australian style points system”. The country’s borders have been tightened to the point that students, engineers, academics and doctors are being turned away – the only types of immigration that command any widespread popular support. So Labour has two options as far as “tackling voters’ concerns” are concerned. It can decide that recession, a closed border between Northern Ireland and the Republic, rising food prices, crippled financial services industry, permanently slowed growth are a price worth paying for the right to have slightly fewer Poles in the service industry. (These may not be the repercussions of a Brexit from the European Union to the EEA or a Swiss-style set of multiple treaties, but would be the inevitable consequence of a Leave vote that saw genuine border control as its absolute end, the approach championed by Ukip and Vote Leave.)

Or it can decide that, whether inside the European Union or in the Swiss-Norwegian model, not having full control of your own borders is a price you pay for entry to the single market. That leaves the not inconsiderable question of how to win power under first-past-the-post on that basis.

Now, that's not an easy question – but it does have the benefit of being a real one, rather than another decade of talking about talking about talking about immigration.