Sunday mornings at Fulham pools is pretty quiet and might be a good option. It's a pain to get to via public transport, from SW, but the drive at 9 or 9:30 is about 12 minutes from Balham.

I would second Putney Leisure centre.

There is a very small, round, heated pool which is great to build confidence and practise jumping in/short distance swimming.
You can then either move to the kids pool (which does have mini slides) or the big pool.

Have you tried Balham Leisure Centre Pool? Its a small pool and nothing distracting unless you go Tuesday afternoon when they have a parent and child fun session.

I used to take mine to Putney leisure centre, which we loved. The teaching pool is not too shallow & as it is completely separate from the main pool there were only little ones with their parents in it. However, that was some years ago so you would have to check availability now, it was occasionally closed for teaching.

My husband has decided to take up the mantle and continue teaching our son to swim rather than using organised swimming classes/a swimming instructor. Our son can do basic swimming already but needs to practice the strokes to become competent so we are looking for somewhere where its not too crowded and where we can get him to concentrate without loads of distractions! So we've pretty much ruled out the Latchmere owing to the elephant slide and the wave machine which are too big a distraction! Just wondered which local pools might suit us better? We've tried Clapham Leisure Centre which is a possibility although the teaching pool is very shallow and the larger pool is a bit cold. Can anyone suggest where else we should try? Thanks!