London is obviously the most international city in the UK, but I don't think the divide is so huge; other big cities are also increasingly diverse, surely - I just haven't seen as detailed a break-down of the statistics for other places.
I'm in a well-off area of a biggish city and my DCs go to private schools (day schools, not boarding), but in DD's class, I would say at least 25 per cent of the children are not 'white British' - some are British but not white, some are white but not British, some are neither white nor British - but they can all afford the school fees. And fwiw, DD is white and British but was not born here so counted as a 'recent immigrant' as far as the census was concerned.
DD's previous state primary, in one of the most expensive areas of the city, was similarly diverse. Lots of nasty lazy immigrants doctors and academics amongst the parents in both schools.