Rachel Reeves joined EU finance ministers for dinner in Washington last week, on the sidelines of the International Monetary Fund spring meetings – the first time a chancellor had done so since Brexit.

It was the latest symbolic step in Labour’s marked shift towards prioritising closer EU relations.

That makes perfect sense against the backdrop of Donald Trump’s reckless Middle East conflict. But domestic politics and economics have increasingly aligned in favour of a lean towards the EU, too – or, rather, Labour has increasingly opened its eyes to them.

As political scientists such as Rob Ford and Ben Ansell have been all but screaming for some time, Labour is losing many more voters to the left wing, pro-EU Greens and Liberal Democrats than to Nigel Farage’s Reform UK.

That is only likely to become more evident when the results of May’s elections come in.

Since the departure of Morgan McSweeney, the government appears to have become markedly more willing to try to win some of these lost lefties back, instead of hankering after Reform-curious “hero voters” – those won directly by Labour from the Conservatives in 2024.

When it comes to the economics, there is a growing body of evidence about the impact of Brexit on what is meant to be the overriding “mission” of the Labour government: kickstarting growth.

In her Mais lecture last month, Reeves highlighted analysis published by the National Bureau of Economic Research and led by Nick Bloom, a British economist based at Stanford, suggesting leaving the EU may have knocked up to 8% off the size of the economy. “Brexit did deep damage,” she said.

That is significantly larger than many previous estimates. Whatever the right number, it dramatically dwarfs the potential upsides from the various non-EU trade deals the UK has struck since 2016.

As Reeves put it: “No trade deal with any individual nation can outweigh the importance of our relationship to a bloc with which we share a land border, with which our supply chains are closely intertwined, and it accounts for almost half our trade.”

Yet Labour’s current painstakingly discussed “reset” in relations with the EU, along the lines prescribed in its manifesto, is likely to be worth less than 0.5% of GDP, according to John Springford of the Centre for European Reform.

That doesn’t mean these negotiations – on agrifood, the EU electricity market and the emissions trading scheme – are not worth pursuing. But it makes sense that Reeves is now looking further – pointing to the possibility of “dynamic alignment”, or automatically following EU rules, in exchange for more access to the single market.

Which industries she has in mind are as yet unspecified, but the government plans to give itself the legislative levers to track changes in EU regulations without putting every tweak to a House of Commons vote.

It is not an unreasonable aim, although in reality Labour’s room for manoeuvre is likely to be limited. Widen the sectors at play too far, and Brussels is likely to object to a non-member “cherrypicking” aspects of the single market. And the greater the economic benefits at stake, the more likely the UK will be urged to accept freedom of movement – crossing one of the government’s cherished manifesto red lines.

The EU has recently renegotiated its relationship with Switzerland, precisely to avoid concerns about a pick-and-mix approach. The new set of deals falls short of full single market membership, but it entrenches freedom of movement and budget contributions.

Anand Menon, the director of the thinktank UK in a Changing Europe, says Reeves and Keir Starmer may be arguing for something undeliverable. “At a certain point, they’re not going to get the benefits without the obligations.”

There is a deep irony here, not lost on veterans of the scarring and chaotic Brexit debate in the 2017-2019 hung parliament.

What Labour is walking itself towards, crabwise, has much in common with Theresa May’s doomed Chequers deal, which would also have involved aligning with the EU in key areas. “Labour would bite your arm off for that now,” says Jill Rutter of the Institute for Government.

Starmer, as the shadow Brexit secretary, played a crucial role in collapsing talks with May’s government over her withdrawal agreement with the EU, not least by demanding a referendum on the deal.

The prospect of collapsing her government was probably too delicious to resist, but the ultimate outcome was the triumph of Boris Johnson and his harder, narrower vision of leave. Labour opposed that with every parliamentary manoeuvre it could muster, and ended up proposing instead to reopen the entire Brexit debate with another referendum – a policy for which Starmer was the torchbearer.

Jeremy Corbyn’s leadership team was by this point exhausted and divided; but the end result of the second referendum gambit was a crushing general election defeat. Starmer’s less-than-deft political touch was evident even then, for those who cared to look.

If the party is now careering towards a leadership contest, the UK’s relationship with the EU will be high on the agenda: some backbenchers are already advocating a “Swiss-style” approach.

That would mean thinking the unthinkable, and making the risky political argument for a return of free movement – a hard sell, at a time when Farage’s well-funded rightwing populists are running riot, and a long way from the prime minister’s “island of strangers” speech.

Any would-be candidate hoping to make that case, though, might take inspiration from the words of another putative party leader, who said at his campaign launch: “We welcome migrants; we don’t scapegoat them. Low wages, poor housing, poor public services are not the fault of people who come here: they’re political failure. So we have to make the case for the benefits of migration; for the benefits of free movement.” That candidate? Not Zack Polanski, but Starmer.