I haven't been to London in a long, long time.. but had a great time there on the visits i have managed. Stayed in Earl's Court.. in a funky, comfy.. and cheap hotel (it's probably not the case now).
The area was filled with pubs, and Australian expats.. very lively. And i did manage ot get out for some high brow stuff on occasion.. museums, galleries, concerts.
The only problems i had with the place was the warm beer, incomprehensible street layout.. and nearly getting killed by looking the wrong way when i crossed a street. They all drive on the wrong side of the road there.
As for 'Cultural Capital of the World'. That's debatable.. New York's got the money. And culture always follows the money.