Against some stiff competition, one of the worst things about Brexit is the way it sucks up all the oxygen, consuming whatever political energy is available, until there’s none left for anything else. Just think what we might have achieved these past three years if the bureaucratic and intellectual resources we’ve devoted to the business of leaving the European Union had been directed elsewhere.

Instead, there’s barely been time to think about, let alone deal with, the climate crisis or even some of the issues that led to the Brexit vote, from precarious work to the shortage of affordable housing. There is, perhaps, no more concrete example of this attention squeeze than in relation to an idea that would utterly transform the public services we rely on from cradle to grave: an idea so bold and innovative it is winning admirers all over the world, its author summoned to address governments from Scandinavia to Latin America, its approach hailed on the opinion page of the New York Times as the “fix” for a broken welfare state – and yet all but ignored by the national government of the author’s home country, whose bandwidth is consumed entirely by Brexit.

It comes from a social entrepreneur by the name of Hilary Cottam. Full disclosure: I’ve known Cottam for years, long before she was named Designer of the Year in 2005 for her work reshaping schools, prisons and health facilities. She was subsequently described as being “to social design what Conran is to sofa design”.

I first met her in Washington in the mid-1990s, where she was ruffling feathers working for the World Bank. The bank’s modus operandi back then was to jet into a distant foreign capital, stay in a five-star hotel, conduct meetings with officials, then sign an agreement for, say, a $140m investment in a dam, before flying back to DC.

Cottam operated in a different way. She would head out of the capital, pitch up in a remote village or township on the outskirts and live for a week or two with the people of that community, talking especially to the women. After one such spell on the margins of Lusaka, Zambia, she heard what people there needed most. It involved water, but it wasn’t a dam. And it cost closer to $140 than $140m. What was it? A standpipe in the centre of the village – so that the women could collect water safely, rather than having to venture to a tap far out of the way, somewhere scary and dark. Simple, cheap – but utterly transformative of their lives.

‘Hilary Cottam was described as being ‘to social design what Conran is to sofa design’.’ Photograph: Murdo MacLeod/The Guardian

Cottam did the same when she was tasked with turning around a failing school in the south London borough of Southwark. She talked to teachers and pupils and found that one reason children were not settling down to learn, why they acted as if they were not fully present, was that they never took off their coats. Why not? Because their lockers were in a badly lit corner where kids were liable to get bullied or beaten up, so no one ever went there. Cottam altered the design, bringing the lockers into the daylight: bullying went down and, thanks to that and a series of other such moves, academic attainment went up.

In the last decade or more, she’s been applying a similar approach to public services. In Radical Help – a book that’s been published from Denmark to South Korea – she describes five “experiments” in different areas of public provision, touching on every stage of life: adolescence, work, healthcare, social care for the elderly and social work for so-called troubled families. These were pilot schemes, backed by local councils who had often grown so desperate at the status quo and so determined to improve the lives of their residents, they were ready to try anything.

Take Circle, a scheme aimed at the elderly. Much of the current discussion about elderly care focuses on budgets and structures, imagining a new multibillion-pound institution on a par with the NHS. But Cottam started with the most fundamental unit of all: a single human being. She tells the story of Stan, a frail 90-year-old man whose main problem was loneliness. He lived in sheltered accommodation and longed to talk to other people, to share the music of his youth. This didn’t require an elaborate new bureaucracy or expensive new council programme. All it took was a volunteer to find a way for Stan to play his choice of Sinatra songs to a few other people down the phone, so they could listen to the music together. It was just five of them at first, but it grew.

Eventually, Circle connected older people with each other in similar ways, seeing the elderly not as a burden to be managed but as a vast potential resource: one might help another with the shopping, someone else might do a bit in the garden or just pop by for a chat. Circle schemes in Nottingham, Rochdale and elsewhere reported astonishing results: those once written off as housebound, reduced to passive recipients of the occasional, state-mandated visit from a health visitor or cleaner, were instead forging friendships, getting out more and finding new purpose in their lives. They became healthier too, turning less often to the NHS.

That’s because many of the problems they had weren’t really medical, they were social. And that is the core insight of Radical Help: that what can turn lives around is not a hulking bureaucracy of targets and tick-boxes, but simple, human relationships. The current welfare state, says Cottam, is a “transactional, pass-the-parcel model”: she describes how one single mother in Swindon had passed through the hands of no fewer than 73 different clipboard-carrying professionals, whether social workers, health visitors or police officers, costing the taxpayer £250,000 a year. And yet nothing got better.

Infusions of cash are necessary but, at best, says Cottam, “all they can hope to do is pass better parcels, faster”. The answer is “social connection”, embedding people in relationships with each other rather than with an often opaque, blundering state.

Some will hear this as a David Cameron-style, “big society” shift away from state provision. But Cottam is clear. The state is essential, both as a financial provider and to set a lead. It’s just that it needs to do its work differently. This, she insists, is not a project of the right but the left. Not for nothing did one Scandinavian newspaper ask if Cottam’s vision was “the antidote to neoliberalism”.

The point is that the 1945 model of the welfare state was designed for a world that no longer exists. It was predicated on the assumption that each home would have a male breadwinner, alongside a woman who would do the unpaid work of care; that that male breadwinner would have a job for life, with no need to retrain; and that life expectancy was short, with most seeing out a few years of retirement before dropping dead, rather than living with chronic conditions that could endure for decades. Since those 1945 conditions no longer apply, it should be obvious that a welfare state designed around them has to change and change radically.

These are the questions we ought to be facing. They belong among the causes of which Brexit was a symptom. Plenty in the UK’s local councils know that; from Wigan to East Ayrshire, they’ve been listening to Cottam. So have governments around the world, aware that these big societal shifts are affecting them, too. But not Whitehall. The only sound it can hear is Brexit, drowning out everything else, including the quiet hint of a better, brighter future.

• Jonathan Freedland is a Guardian columnist