Accepting the Olympic flag yesterday at a lavish closing ceremony in the Bird's Nest stadium, Boris Johnson promised that London would draw on Britain's wit, flair, imagination and ingenuity to build on the success of the Beijing Games. The Mayor also spoke of his immense pride in the athletes, in the people who delivered the Games' success and in the challenge of London accepting the Olympic legacy.

Britain's athletes flying in to heroes' welcomes at Heathrow today will be four years older and perhaps a little wiser come 2012. In principle the same goes for London, yet wisdom is not immediately evident in what it is setting out to do. Defiance may be closer to the mark.

London will be hosting many of the same competitors striving once again for medals. It will boost them with home crowds but burden them with more pressure than ever to win, and it will ask taxpayers for at least £9.3 billion to lay on what Lord Coe and Mr Johnson promise will be a “fantastic” Games - even though both have acknowledged there is no point in trying to surpass Beijing in terms of scale or the opulence of its venues.

The task, in fact, is to reinvent the Olympics on a budget roughly half the size of Beijing's. It is a huge challenge, yet not quite as daunting as it sounds. Beyond the basic requirement of staging a major competition for all-comers in more than 120 sports, the long-term goals of the two cities are very different. Beijing's political purpose was to announce China's ascent to modernity and world power status. Its legacy will consist of national monuments and, if the world is lucky, a gradual Chinese perestroika.

The London Games, too, will have a political goal, but the more modest one of energising and empowering a nation's youth. As Lord Coe has said: “We want fewer couch potatoes and more participants.” Were he still an active politician he might have added: “And fewer ASBOs.” The Games' legacy, on paper at least, is to be the renewal of an area of East London that other urban regeneration schemes have failed to reach.

Despite these differences there are important lessons that London 2012's substantial delegation to Beijing ought to be bringing home. Like Beijing, London must share the games with the whole country. Weymouth will host the sailing. So let Badminton, Burghley or Chatsworth host the eventing (saving Greenwich Park possibly irreparable damage in the process), and take radical steps to ensure venues are filled with people who want to be there rather than crowds bused in for the cameras. This will require proactive marketing months - if not years - in advance, sensibly priced tickets and flawless logistics, since the second lesson from Beijing is that even enthusiastic fans can be deterred by the fear of chaotic crowds and opportunistic pricing.

Simon Clegg, the head of Team GB, has said the success of the Games in 2012 will be judged “not on how efficient the transport is or what the stadiums are like, but on how many men and women stand on the podium with medals round their necks”. But this is only true if that transport and those stadiums are world class.

On its ill-advised torch relay, the Beijing organisers exacerbated tensions with a phalanx of stone-faced runners protecting the flame. At home they fared better, creating the illusion of relaxed officialdom and light-touch security.

London must achieve the same outcome but without the advantage of a one-party police state. It can and must be done, but only with a feat of collective exertion and enthusiasm that will strike many as unfashionable and downright un-British. But it would be far worse to fail. The countdown to 2012 has already been going for three years. There is no time to lose.