How old is your DS and do you mean for him to start this year? State school places have already been allocated for September.
Lots of private schools offer plenty of extras so it might be worth checking out any near where you live. State schools sometimes do after school sports classes, ours does football, tennis, mixed sports and gymnastics as well as french and spanish lessons (at a cost.)
My DDs go to state school and do other activities as well. It should be easy enough to find an afternoon sports club, swimming lessons, drama lessons, art, etc.
He has a place at a state school for september in Islington. I think Reception will be fine, learning through play and all. But I'm not confident he'll transition well to Year 1 as I've seen it in practise and he is just not suited to it. He is very physical and being constrained in a small classroom and playground does not suit him well.