London has a lot of pools and Lidos but it also has a lot of people, so swimming in the city can be stressful. I have spent a lot of time in the Clapham Leisure Centre (25M). I did have a large gap in-between visits where unknown to me it had been knocked down and rebuilt which was a little disorientating. This is a nice facility but doesn’t have very many lanes. Clapham is full of people wanted to exercise so pick your times wisely.
When I lived in South London I would go to Brockwell Lido which is lovely in the Summer. I did manage to get hypothermia during one early spring training session, so I have mixed memories!