There's also outdoor swimming at Hampton. Of the indoor pools, I guess the nicest is the one in Mitcham (Canons Leisure centre), but there's one at the leisure centre in Wimbledon (Latimer Road) and another at Morden Park (also a good place to run - that is, the park, not the pool). In Earlsfield you're very close to Wandsworth Common and, from there, to Clapham Common (but it's uphill to get there) - and not that far from Wimbledon Common and Morden Hall Park (not the same as Morden Park). Worth stretching your legs and getting out to those places.
Of course, that's assuming that going private is better than the state system. My considered opinion is that it's not. That people from private schools get better jobs is, to my mind, a condemnation of our social and political system, not an argument in favour of private schools. Anyway, it's clear that people who go to public schools and Oxbridge have way too much influence on Westminster. Just my view.