“Oh, to be in England / Now that April’s there,” wrote Browning, but he might have looked at that again after last weekend and decided it could bear revision. “Oh, to be in England’s capital as Gareth Southgate’s team march nonchalantly into the World Cup semi-finals,” perhaps. When people meet the glances of others, smile and know exactly what they are thinking. When strangers, merry and giddy, connect on the trains that usually symbolise an urban dystopia. When young Britons of many complexions sport England shirts and look as though they had won a modest bet.

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Sure, there was over-exuberance: “Two world wars and two world cups,” was one mindless chant as my train circuited east London. Some drink-fuelled boorishness. The idiots are out there: football wakes them from their slumber. Across the UK, 70 got themselves arrested. But they haven’t set the tone.

Twice I’ve heard: “Oh God, the Brexiters will love this.” Not the decent millions who for one reason or another saw a better life outside the EU but the fundamentalists – the Rees-Mogg tendency, the Faragistas – whose pursuit of a reactionary English nationalism has poisoned the national debate. They will claim this, was the lament. But they can’t.

Because there is nothing about that team, with its youth and vigour and diversity and modernity, that would give nationalists any succour. What can they credibly say about a team born of the contemporary Britain they so despise, with its thoughtful, dignified manager, its melding of young men whose lineages originate far and wide – not least the Windrush generation grandchildren? What’s pleasing about the England campaign so far is that it is a project that looks ahead. How can it be claimed by reactionary Brexiters whose only navigation tool is the rear-view mirror?

England may not prevail tonight but already they have given us a moment. And isn’t that something for the government to think about? It can’t mandate bonhomie, but it can think again about the power of sport to create moments when a diverse society finds common cause. And then it can start funding grassroots sport properly through the public purse on the basis that it yields public gain. It can take a hard line to ensure that events that drive a national mood and conversation are accessible to all, not just to those with pockets deep enough to view them via satellite dish or premium cable.

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It can think seriously about how and where and why those communal moments occur and what might be done to have more of them. A diverse nation is a boon in the modern world. It is a fact of life. But it throws up challenges. Homogeneity is a thing of the past. Someone in government has to be thinking about the ties that, day to day and then on special days, bind us together?

The World Cup shows what can be achieved, as did the 2012 Olympics. They don’t endure, but they offer a glimpse of possibility. Oh, to be in a land that knows itself – and knows how it can be happy.

• Hugh Muir is a Guardian columnist