The opening ceremony, by common consent, was the best in memory. The London volunteers have been utterly tireless and infectious in their enthusiasm; the venues have shuddered to the noise of the crowd, skilfully whipped to fresh pitches of excitement by the masters of ceremonies. Across London there has been a happy maelstrom of parties and celebration, of a kind that they tell me was to be found in Sydney – except that in London it has been everywhere, and not just in the centre. Yesterday I cycled down the canal towpath to the Olympic Park, through Hackney; and everywhere I looked there were scenes of riparian merriment of the kind you expect to see at the Henley regatta. The reason for this outpouring of joy is very simple, and it is not just that people are conscious that this country has put on a great show.

It is the Team GB athletes who have stunned us, and the rest of the world, with their astonishing haul of gongs. Never in my wildest dreams did I think that British athletes would end up with 29 gold medals, or that Team GB would be in third place behind America and China. We have not only dwarfed the Beijing tally. We have decisively laid to rest the ghost of 1948, when we last hosted the Games in London, and an undernourished and exhausted British team could barely scrape together three gold medals, and came 12th – even though Russia and Germany did not even turn up.

As everyone now knows, this is the biggest British medal total since 1908, when we featured events such as live pigeon-shooting and a tug of war. But not everyone perhaps appreciates that in 1908 we did not exactly behave in a spirit of undiluted sportsmanship and fair play. Seizing host-nation advantage, the British more or less eliminated much of the American competition by forcing them into the same heats; and as for the famous victory in the tug of war – which went to the City of London police – it pains me to relate that the police were allowed to dig in with their hobnailed boots, while the American finalists were left to scrabble desperately for purchase with their plimsolls. They protested at the unfairness of proceedings – to no avail.

This time it is different. In 2012, Team GB has been sporting, generous to their opponents, and propelled by no stimulant more sinister than McDonald’s and Coca-Cola; and yet they have won far more gold medals per capita than their closest rival teams from America, China and Russia. It is a staggering performance, a tribute to the athletes and all who have helped them on the way.

As we marvel at what they have done, and the general success of the Games so far, I want to issue a general word of caution to the Olympo-sceptics, who will be itching to return to their gripes. They will say there will be no increase in sporting participation, and no economic benefits, and that we will not succeed in regenerating east London. Well, just remember one thing, everyone. These Olympo-sceptics were proved decisively wrong about the Games. They will be proved wrong about the legacy as well. These Games have not changed us. They have revealed us as we are: people who can pull off great feats.

London has put on a dazzling face to the global audience. For the first time since the end of the empire, it truly feels like the capital of the world.