Just got back from the Chow-Agee London Tour 2010! It was a fantastic vacation, and I only gained 5 pounds (no, not money!)!
There is a GREAT place to swim. Keeping in mind that you can find pools anywhere, I highly recommend swimming in the Serpentine at Hyde Park! Now that is something you can't get at home!!! It's mid-way along the park, right by the Lido (restaurant). It's not well marketed and I didn't find much about it on the internet, or even expect it be open, but it was great!
First, most families are splashing it up at the free Diana Memorial water fountains. It's a madhouse and way too crowded. We forked over just under 13 pounds to swim in a roped off area in the Serpentine. There were very few people there.
For lap swimming, (although I didn't swim it) were 2 roped off lanes that I would guess were a bit longer than 50 meters. The closest I got was helping some chap zip up his wetsuit. I pretty much goofed around instead. My girls loved it! It's not everyday they get to spend an hour chasing ducks in the water, and they pretty much had these ducks all to themselves (and why they put up with my girls I don't know. Probably some pavlov thing and they kept expecting to be fed instead).
There is also a playground area (actually, it was pretty lame, but since it was only for us paying customers, i'd have to rate it higher for being empty) and a baby pool. There is a grassy area to sit, and there are changing rooms. You could get a small locker for 20p (coin comes back out, so don't forget to retrieve it!) and you could rent a towel for 2 pounds (way too steep, bring your own!)
It was open 10-6, with a cheaper rate after 4PM. It costs 4 pounds per adult, 1 pound for children. A family rate (2 adults plus children) is 9 pounds. The Duggers would practically make money on that deal. However, we went right after 4PM and got 2 adults, 2 kids, and my sister in for about 12 pounds due to reduced afternoon rates. Sorry, didn't catch the season dates.
Our apartment was 1 street off at an entrance to the park (Lancaster Gate); it took about 15 solid minutes to walk there. It's not a bad walk, but it woud truly be the Walk of Shame if you forgot your swimsuit and had to go back to get it. Any of the tube stops along the park would be fine. Nothing is super close, and none are too far to enjoy the walk.
It was one of the highlights of our trip because it's something you wouldn't typically expect to do in London - swim in the lake of a famous park, and overlook the paddle boats plus have it practically to yourself!!