It has never been difficult to contrast the douce town centres across East Lothian with the bustle of London.

Having spent a week smack in the centre there (the Royal Opera House just across the road), it is clear that frequent trips and having lived there for years are still inadequate preparation for how fast life moves on here.

As with Edinburgh, July grows hectic, with polyglot crocodiles of teens displaying boundless enthusiasm and scant understanding clogging most tourist destinations. American visitors stand out from more fashion-conscious Europeans by their uniform shorts-and-baseball-cap.

But, as with much else, it is the scale of things that astonishes: Covent Garden is a sea of people; queues snake out of St Paul’s Great West Door and round into Paternoster Row; even the hard-to-find Imperial War Museum buzzes with youth from ex-colonies and ex-enemies in equal numbers.

But the buzz of the city is well beyond pre-2007-crash levels. Congestion Charging has filtered out most cars but delivery vehicles, buses and taxis fill sclerotic arteries. The overcrowded Tube is oppressively tropical. Pavements are alive with purposeful people, many smoking and intent on business. Hidden pubs like the Lamb & Flag on Lazenby Court or Ye Olde Mitre on Ely Place are jammed by expensive suits, ties akimbo talking intensely about work.

Contributing to a hefty noise level are building sites round every corner. The massive £15bn Crossrail project has pockmarked craters across the city. But most notable is a skyline sprouting cranes – 21 along Oxford Street alone. Buildings that were new three decades ago are being replaced. The architectural cacophony on some streets is jarring but unspoiled oases of cohesion – Georgian Belgravia, Regency Bloombury, Victorian Marylebone – survive, celebrating very liveable styles.

Unlike Edinburgh, serious investment in road renewal is under way, including arteries like Waterloo Road. Unlike Paris, there seems no slacking of the city pace as people disappear on vacation. Unlike New York, the action happens across the centre without no-go areas like Harlem to be avoided.

The net effect is vibrancy seldom seen before in Britain. From a pulsing capital of a global empire, London has evolved beyond the relative parochialism of most front-rank cities, surpassing New York in diversity, Paris in culture, Tokyo in business to become perhaps the first real cross-cultural global city the world has ever seen. We Scots could learn from its dynamism and prosper with its results.