The London Olympics have been both a resounding sporting and a cultural triumph. Taking place against the backdrop of the Great Recession and the worst economic crisis since the 1930s (as well as one of the wettest summers in living memory), and with the secessionist Scottish National Party agitating to break up the Union in 2014, the Games have helped to redefine notions of patriotism and Britishness. A year after England was ravaged by urban riots, they have been a glorious distraction from our economic troubles and from the squabbling of our fractured, directionless and increasingly unimpressive coalition government.

But the Games have been much more than a distraction – they have created a sense of national unity and purpose and, at times, a kind of ecstatic sociality. The torch relay around Britain showed, even before they began, just how much enthusiasm there was for the Games among the general population. In an age when our lives have become so atomised, the yearning for the shared experience clearly runs deep.

Encouragingly for the Labour Party, as it begins the long, difficult journey back to power and seeks to remake social democracy for an age of austerity, the Games have restated the case for a strong and competent interventionist state. The conservative right distrusts the state: the market remains the one true arbiter of value.

Yet only the state can redistribute wealth to the benefit of the many and not just the few, challenge cartels, regulate financial services and create the economic conditions to power growth and invest in vast infrastructure projects, such as the Olympics. As Barack Obama said, in a recent speech in which he made the case for strong government: "The point is . . . that when we succeed, we succeed because of our individual initiative but also because we do things together. There are some things, just like fighting fires, we don’t do on our own. I mean, imagine if everybody had their own fire service. That would be a hard way to organise fighting fires . . . We rise or fall together as one nation and as one people."

Indeed, renewed state investment in school-building programmes, in school and recreational sports facilities and in nationwide transport infrastructure should be one of the legacies of these Games.

London 2012 has also been a celebration of the cultural and ethnic diversity of contemporary Britain. The Danny Boyle-directed opening ceremony, Isles of Wonder, was a triumph of wit, invention and iconoclasm. It was utterly original because, free from bombast and the old imperial anxieties, it sought to remind the British people and the world what is best about the complex, multinational, multi-ethnic and multicultural nation state we call Great Britain. Forget for a moment how much it all cost and enjoy its lasting resonances.

It was thrillingly appropriate, too, that a Muslim named Mohamed – who was born in Mogadishu, Somalia, and came to London as a young boy – has emerged as one of many British heroes. A Londoner and ardent Arsenal fan, Mo Farah knows who he is and what his home city and country mean to him. When asked in the aftermath of his triumph in the 10,000 metres, on the evening of Saturday 4 August, if he would rather have been representing Somalia, Mr Farah said, in his engagingly chirpy London accent: “Look, mate, this is my country. This is where I grew up, this is where I started life. This is my country and when I put on my Great Britain vest, I’m proud. I’m very proud.” Quite so.

In an interview with George Eaton on page 24, Tim Soutphommasane, a young Australian thinker who is close to Jon Cruddas, the MP leading Labour’s policy review, outlines his vision of a new progressive patriotism. “For a lot of people [on the left], patriotism is, by definition, an exclusive and a very nasty sentiment, when there can in fact be a very appreciative and generous love of country,” he says. We have witnessed that generous love of country throughout the Olympics; witnessed the outpouring of a soft and benign patriotism, quite different from the hard, defensive patriotism of the Eurosceptic right or any number of Little Englanders or some Scottish nationalists.

In Britain, we do not have an independence or Bastille day to celebrate, as in the US or France. But at least we have had the London Games to remind us, if we needed it, that we do not necessarily have to create a new, post-imperial British patriotism to bind us together in all our diversity: it already exists and is instinctively understood by many millions of people, including one Mohamed “Mo” Farah.