I live in the inner suburbs of North London (about 5 miles from the absolute centre) and don't really recognise any of those problems. There's loads of kids here - literally every 3rd house on my road has a family with young kids in it. Nurseries are no more crowded than other UK cities either. Obviously there's some level of crime - but that's also present everywhere to varying degrees. There's loads of kids activities here as well.

The city isn't a single place - it's a whole load of historical towns and neighbourhoods joined together. Experiences vary.