ONE world, one dream. The slogan of the XXIX Olymp-iad is omnipresent in Beijing. When the closing ceremony ends with fireworks over the Bird's Nest tonight, there will be remarkable unanimity that these Games have achieved more than anybody dared to expect.

Yet they got off to an inauspicious start with a relentless attack by the Western media on China, and hostilities breaking out between Georgia and Russia within hours of the opening ceremony. Not so much a world dream as a planet-ary nightmare. But over the past fortnight the critics have been increasingly silenced if not entirely appeased. Despite the media's professional cynicism, the international legacy of Beijing will be a more rounded understanding of this emerging superpower.

In return, China may have come to realise that it needs to make concessions to world opinion on human rights. It's easy to attack the Olympics, and many have, but the last fortnight has laid the base for greater understanding between east and west, whilst the domestic bonus for Beijing is the modern-isation of this huge city and cleaner air for its citizens.

The sport hasn't been too bad either. The venues have been magnificent, and the daunting logistical operation has been run with the efficiency you would expect of a ... well, a totalitarian state. It's a giant ideological leap from communism to Old Etonians, but if, as now looks likely, David Cameron and Boris Johnson are running Britain and London in 2012, they have got an awesome job to offset memories of the grandeur of these Games.

The athletes responded to the superb facilities with a plethora of world records in the flagship sports of athletics and swimming. We had the American, Michael Phelps, who was feted as the icon of the Olympics by IOC president Jacques Rogge even before he had notched his record eight gold medals (seven of them world bests). But then Usain Bolt emerged on the track to challenge Rogge's assessment. Personally, I'd call it a dead heat.

There were 21 world records in the Water Cube alone, and athletes are continuing to swim and run faster than ever before. Phelps, a down-to-earth American from working class roots, and the Jamaican Bolt, who is much more of a showman, provided wonderful memories. So far, at least, there is no suspicion that either is tainted by association with illegal drugs; this is particularly important for athletics, a sport which badly needs a clean sprinting hero.

Those looking to nit-pick will point out that the atmosphere inside and outside stadia did not match that, for example, of Sydney, and I'd concur with that assessment. The Chinese, for all their great success in the medal table, are not yet a society steeped in sport and don't have the depth of knowledge which is found in Europe, the Americas and Australasia. There was passionate support for the home athletes, but otherwise, and particularly in the Bird's Nest, enthusiasm and appreciation for the efforts of other athletes could have been better.

But what an effort by China. Most expected the hosts to top the medal table, but not quite the manner in which they surged out of the blocks and headed the mighty Americans from start to finish. The Americans won more overall and will claim victory, but the traditional Olympic way is to measure the most successful nation by its number of gold medals.

While the Chinese take the kudos, the Games were also spectacularly successful for Team GB. Twelve years ago in Atlanta, the British retreated across the Atlantic with their tails between their legs, having succeeded in attaining just one gold. That, for the record, was won by the trusty partnership of Steve Redgrave and Matthew Pinsent in the coxless pairs.

Britain was a hopeless 36th in the medal table, but 12 years later the team have been jousting with the Russians for fourth place. The total of 46 medals is even better than the target the team's paymaster, UK Sport, were aiming for - 41 - before the Games started, but there have been two even more pleasing aspects. Firstly, the 85% success rate they were reckoning on has actually exceeded 100%, and, secondly, the number of golds - 19 - has greatly eclipsed the expectation of 12.

If Phelps and Bolt have been the Games' icons, Britain has had Chris Hoy. As the UK dominated the velodrome, taking seven of the 10 golds, Hoy emerged as the first British athlete in 100 years to win three at a Games. His success, and that of the cyclists, was a vind-ication of the vast financial and organisational resources behind the GB team.

More than £235 million of National Lottery and Treasury money was distributed by UK Sport in the four-year cycle since the Athens Games, with £120m of that being disbursed to athletics, cycling, rowing, swimming and sailing. That is serious money by the standards of any country other than China and America, and its scale led to serious wailing and gnashing of teeth in Australia, especially. But by making the money dependent on performance, and investing huge chunks of it on world-class coaches and sports scientists, the gamble paid off.

Given that Britain had effectively two teams in Beijing - the podium athletes who were expected to compete strongly for medals, and a shadow squad who are gaining Olympic experience for 2012 - the realistic expectation now is that the team should do even better on home ground. Before these Games, the ambition was to finish fourth in the medal table in London, but as that will have been achieved here what are the new expectations?

Dave Brailsford, who is performance director of the cycling team, was perhaps inebriated with success when he stated that Britain should be aiming for second place in London. He was correct to reach for the stars, but the emergence of China means that, for the foreseeable future, there are realistically two sports superpowers, followed by the remainder. The secondary race is to see who finishes third.

The performance of host nations traditionally falls away in subsequent Games, but Simon Clegg, the chief de mission of the British team, believes China are here to stay. "Will the Chinese be able to sustain their success?" he repeated in response to my question. "Probably more so than any other country, because of the volume of people and the national pride associated with their successful athletes. Any drop-off is likely to be much smaller than any host nations in the past, and it's a realistic possibility that they may continue to improve further, because the seven years they had in the build-up to Beijing is not long in terms of high performance sport."

Clegg, who is naturally cautious because he knows the media will pounce on predictions which aren't delivered, wouldn't commit himself to a new medal table projection for London, but did suggest that 30 golds might not now be unrealistic. But then canniness returned, and he warned that many other nations would be noting Britain's performance in Beijing and seeking to emulate it.

"There is no room for complacency," he warned. "Other countries are looking at us as a good working model and will start to replicate that in their own programmes. We are constantly going to have to push the boundaries. Just because we've had great success here doesn't guarantee great success in four years' time.

"At every Games more and more countries are winning medals and aspiring to success. They understand the national pride that comes with that, and more and more money is being pumped into high performance systems. There's no such thing as an easy Olympic gold medal.

"We need to keep supporting our outstanding systems in cycling, rowing and sailing, which have delivered in bucketloads, but we can't just be dependent on these sports. The encouraging signs are that we're starting to do better in others."

If these Games have done nothing else, they have raised sport up the political agenda in China, Britain and many other countries. There must be a social legacy too, in terms of more people becoming physically active and leading more fulfilling lives. That alone is worthy of the Beijing slogan, and also achievable.