....argh! Mobile phone decided it would post for me.
As I was saying, London has lots of excellent schools that offer an enormous range of extra-curricular activities. My DDs' state primary offers choirs, football, basketball, sewing, rock band, music ensemble, brass, woodwind and violin lessons, debating (Y5-6) and various different clubs across the year. It's nothing like a private school though! Results are very important and the school are under pressure from the LA all the time which leads to before/after school booster classes for the poor Y6 children. In a private school, the LA have no say in what happens. In state schools, teachers are paid properly, receive ongoing training and are expected to implement endless policies at the drop of a hat. Private schools make up their own curriculum and pay scales and some offer little in the way of teacher training. Private school uniforms round here seem to include strange hats and wool blazers. A number of the local state schools don't have a uniform. From my experience of both sectors, I'd say that state is likely to offer a greater pool of friends as the classes are usually bigger and the intake more mixed.
Apart from not having to wear an Enid Blyton-esque school uniform, I believe my DDs are receiving far better teaching at their Lewisham state school than I've seen on offer at local private schools.
Don't be swayed by private schools saying they work a year ahead of state schools, they are often out of touch with reality.
Apart from issues of uniform I wonder if you'd like Brindishe Lee, Halstow or Edmund Waller schools in Lewisham and Greenwich boroughs.