What are your plans for secondary, bossykate? State secondary schools generally have a wider range of after-school activities than the primary schools do, and by that stage the children could make their own way to them.
My knowledge of private schools is fairly scant (derived from knowing a very small number of pupils/parents, driving down the South Circ, and a very occasional glance over to The Other Side ) but I'd observed that:
If you went straight for the junior section of the huge school that dominates the landscape, then entry to the senior part is automatic, but the fees are higher that way.
Flowery alcoholic place frequently appears in the local press for a pupil getting the top scholarship to the huge school, and there's quite often a big banner outside at the right time of year saying all the pupils got into their first choice. They have a number of good chess players.
Grassy tree place seems to equip pupils with more than ample vocabulary to go into the state sector, which some pupils do. Having said that, the school really did a lot for DS1's friend, whose talents were not recognised at his previous school, and he didn't change in the way some children do when they go to private schools.
I'm surprised you're not closer to the schools on TheBlonde's recent thread - but perhaps you have reasons for avoiding those? (I think I can see a few....) For somewhere that may have less of a gulf to bridge from where your son is now, what about the Norwood nuns? (I suspect you may tell me I'm jumping to a huge and totally incorrect conclusion here...)