The Grand Slam breakthrough of Andy Murray in New York rounded out a tidy 24 hours for British sport on the global stage. And none of this had anything to do with the Olympic movement. The day before Murray's epic conquest of Novak Djokovic, Rory McIlroy was busy colonising a verdant corner of Indianapolis just as he had in Boston seven days earlier, winning a second successive PGA Tour event in the lucrative FedEx play-offs. In northern Italy, Lewis Hamilton struck a few hours earlier with a first career victory – pole to flag no less – at Monza, the sacred home of the Italian Grand Prix.

Conditioned by years of international subordination on the football pitch, we have all too often overlooked British – and Northern Irish – excellence elsewhere. The supremacy of our sportsmen in the core disciplines of tennis, golf and motor racing is a non-Olympic reminder not only of the central importance of sport to these isles, but that we are not half bad at it across the canon.

In a sense an appreciation of this broader competence at elite level has been lost in the glow of the unforgettable Olympic gold rush of the past six weeks. The point made by Hamilton, McIlroy and Murray – yes I know he won gold at tennis – is that we were already excelling before the Olympic flame was lit. Bradley Wiggins had in July become the first Briton to claim the Tour de France, Murray himself had contested the Wimbledon final. McIlroy was a US Open champion at 21 and has since added a second major at the US PGA. Hamilton was the youngest to win the Formula One World Championship when he conquered that peak in 2008.

It is not, therefore, as if we needed the Olympic experience to underwrite our credentials as a nation of truly global sporting significance. Of course, we would be equally euphoric were Roy Hodgson to plonk the Cross of St George on the centre spot at the Maracana in two years' time to proclaim England champions of the world. Football is the pre-eminent global sport, after all. The evidence suggests there is not a snowball's chance in hell of it happening, but that does not diminish our standing as a world-class sporting nation.

Was it only a fortnight ago that our cricketers lost their No 1 billing? Do we not approximate to a super-power in rugby? In any given period, Britain boasts boxers with world-title belts. There is not a sport we won't have a go at. Darts? Snooker? Crown green bowls, anyone? Bring it on. We have even produced a decent downhill skier from Surrey. And if Ed Drake had half the funding our cyclists get, you might even have heard of him. Never mind, a spot on Ski Sunday awaits when he tires of paying for his own ski passes, and perhaps a slot on Celebrity Come Dancing. He's blond enough, and tall enough, and handsome enough.

Murray does not owe his success to the British tennis infrastructure, but he is most certainly in debt to the sporting traditions of this country. Hamilton similarly paid his own way, or rather his father did, at times holding down three jobs to meet the rent in his Stevenage home and funding the purchase of a kart for his son to race. McIlroy's old man worked in the bar at Holywood Golf Club, a modest enterprise on the outskirts of Belfast. McIlroy did have generous assistance from the Golf Union of Ireland, but what is that if not an institution born of a sporting heritage?

At some point our footballers will catch up. There is simply too much expertise elsewhere for it not to trickle down into the beautiful game. Already the top Premier League clubs have installed first-rate support mechanisms offering the best that medicine and sports science can provide. The east end of Manchester, with the Etihad Stadium at its heart, is being transformed into a pioneering sporting complex, financed by Abu Dhabi oil wealth. Roy Hodgson's England are showing embryonic signs of improvement, better organised with greater flexibility and enthused by youth.

Our top clubs have, since the inauguration of the Premier League, traded blow for blow with the best in Spain, Germany and Italy. They might have used up a lifetime's luck acquiring it but, nevertheless, Chelsea hold the European Cup. At club level at least, only Barcelona and perhaps Real Madrid might sensibly lay claim to hegemony.

Murray's success is seismic, the first British man for 76 years to win a Grand Slam singles tennis event. It has already been felt in football circles via the presence at Flushing Meadows of Sir Alex Ferguson, who watched alongside Sir Sean Connery. Yes, the Scottish connection was significant, but more than that their attendance was another illustration of the importance of sport to the people of this country. Fergie and 007 chose Queens over Manhattan for their evening's entertainment, a Bud over a Bordeaux. Say no more.