Imagine a family stuck in a house that constantly floods. The carpets are soaked, the walls damp. It’s always cold, no matter how much they turn up the heating.

The family try everything. They promise to replace the sodden carpets and find new, innovative ways to warm the house. Someone with a laptop wonders if AI might be the answer. But no one ever looks upwards and says: maybe we should just repair the giant hole in the roof.

Britons are that family – and the giant hole in the roof is Brexit.

On Wednesday, Rachel Reeves will deliver her second budget, on which, it is widely assumed, the fate of an ailing Labour government depends. Recent weeks have brought conflicting signals – a rise in income tax rates floated, only to be reversed – but there is one big thing we already know: the country does not have enough money to pay for all that it needs and wants.

Every public service you can name is desperate for more cash. Take, almost at random, Britain’s prisons: overcrowded, understaffed and saddled with boxes of paper records, a system so “archaic”, according to the prisons minister, that as many as three inmates are mistakenly released each week. It’s the same story everywhere, from the NHS to the armed forces: we need more money than we’ve got.

Reeves will scrabble around to find a few billion, but none of those efforts will address the fundamental problem, which is that we are poorer than we should be, poorer than we were and poorer than our peers.

Real wages have barely risen in 17 years. Of course, the crash of 2008 was a global phenomenon, but we are struggling more than our counterparts to recover: indeed, for nearly two decades, Britain has experienced the biggest slowdown in productivity growth in the G7. Reeves and Keir Starmer could see the problem when they arrived in office last year, which is why they made growth their paramount objective. But in Britain that is proving stubbornly difficult to achieve, no matter who is in Downing Street.

Of course it is: there’s a great big hole in the roof. This week, the economists John Springford and Andrew Sissons published a detailed analysis examining the roots of the trouble. The UK’s woes, they explain, stem from having too few internationally successful industries: “It means many places have too few well-paid jobs and too little income coming in.”

And why might that be? “Since Brexit, [Britain] has been actively undermining its [own] economic model, which is founded on openness to trade, ideas and people.”

Openness is the heart of the matter. Britain flourishes when it is open and trading, and shrivels when it is not. Brexit ignored that core economic reality – a defining fact about these islands – by making the UK less open to trade in goods, taking us out of a single market in which Britain had been in its element, trading freely and without friction to hundreds of millions of consumers. Naturally, and wholly predictably, “Britain has fallen behind peer countries since it lost access”, write Springford and Sissons, with the fall in goods exports draining more than one percentage point from GDP each year.

The picture is better in services, but even there, for long stretches of the Brexit era, the UK has lagged behind Germany, France, Spain and Italy. Where once we might have relied on the money machine of the City to plug the gap left by a declining goods trade, the finance sector has also been hit, losing its once disproportionately large slice of the market. Frankfurt, Dublin, Amsterdam, Madrid, Milan and Paris have all gained, as London has fallen behind. Incredibly, the capital, once the UK productivity engine that helped the rest of the country make ends meet, is now Britain’s worst-performing region in terms of productivity growth. Given Brexit stripped the City of the easy access to EU clients it once enjoyed, that’s hardly a surprise.

Of course, the decision-makers know all this. Last month, the governor of the Bank of England warned Brexit would have a negative impact on the UK economy for the “foreseeable future”. Previously, the Office for Budget Responsibility estimated that our departure from the EU would shrink Britain’s long-term productivity by about 4%.

And yet, our leaders continue to work around these glaring facts as if they weren’t there – like the family wringing out the drenched carpets, studiously ignoring the hole in the roof above their heads. True, Reeves did at least mention Brexit as one of the causes of the fiscal bind she finds herself in, adding that the government was “unashamedly rebuilding our relations with the EU” to improve the situation.

Would that that were the case. Instead, Labour has made only tentative steps in that direction. The much-vaunted trade deal agreed with the EU is forecast to yield £9bn by 2040. Better than nothing, but for an economy whose value is measured in the trillions, it’s small change.

No, if Britain wants to remedy the ailment that has made it the sick man outside Europe, it needs to be bolder. Rejoin the single market for goods, urge Springford and Sessions. It’s not as if we want to regulate goods much differently anyway, so any sacrifice of supposed sovereignty is negligible.

If that medicine seems too strong, then why not re-enter the customs union? Being on the outside is estimated to be costing us up to £30bn a year, the kind of money that could really come in handy. Admittedly, Labour’s manifesto ruled out such a move, but Reeves was seemingly ready to break her pledge on tax rates – and a U-turn on the customs union would cause a fraction of the political damage. Besides, it could be embedded in a larger argument: that given the straitened times, and the threat posed by Donald Trump’s tariff attack on the global trading system, it is a necessity born of a radically altered situation.

The point is, tinkering won’t cut it. Seasoned Europe-watchers explain that EU officials, many of them shaped by years of attritional Brexit talks, respond to timid, footling proposals from the UK in kind. But if Britain were to be more ambitious, seeking a genuine and bigger reset – putting “more cards on the table to build political momentum”, as former foreign secretary David Miliband put it this week – then heads of government are more likely to push the Brussels bureaucrats aside and get stuck in, forging with Britain a new deal that could be much more profitable for everyone involved.

Again, it is a case that could be made forcefully and that much of the British public would accept – that the world of 2026 is entirely different from 2016, that the old red lines no longer make sense and that Brexit was a waste of money that, now more than ever, we simply cannot afford.

I don’t expect Reeves to say any of those things, but she should. Charged with stewardship of the public finances, she needs to point to the obvious source of so much of our trouble. We blew a hole in our roof a decade ago – and it’s long past time we fixed it.

• Jonathan Freedland is a Guardian columnist

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