I lived in London nearly 20 years and yes it's like everywhere. In Piccadilly Circus or somewhere else busy, of course the shop keepers will be tense and the 'locals' in the pubs won't be looking for a chat (though that is a lie I've had random chats with both on many occasions), but in my own part of east London I'd meet loads of randoms in the park or the pub or the local shops or cafes, esp since having a child.

That said I've now moved to a very small town and it is crazy friendly, people will go out of their way to chat to you and be nice (but then again there are plenty of grumpy shop keepers and locals)

So I guess it is the same everywhere - your own little view will be coloured by your own expectations and by how much you are genuinely open to talking to people.