Have a look at Water Life Swim School

http://www.waterlifeswimschool.com/

The proprietor, Lizzie, is a local mum who runs a variety of lessons at a variety of locations locally, one of which might suit your requirements.

Putney leisure centre has two shallow pools suitable for children including a small round pool that is as warm as a bath.
They also run classes there but I'm not sure of cost.

Clapham leisure centre has a class in their baby pool that is a lot cheaper than other ones yet still very good & the facilities are excellent and clean.

Hi Jana

If you're looking for a small, warm pool locally then I highly recommend the Wimbledon Leisure centre pool which is a 'Better' facility. It's very warm and small so feels safe and my two boys love swimming there. It's cheap for kids and there is free parking in the road behind. My son does lessons there and absolutely loves it. The younger one loves it too, just going in with me.

http://www.better.org.uk/leisure/wimbledon-leisure-centre

Hi mums,

I am thinking of starting taking my 4 months old daughter to swim. All those classes starts in January and to be honest, not sure if I want to pay all that money.
What I am looking for is a swimming pool in south/southwest of London, where is children area, with shallow pool with warm enough water, that I can take my baby there and enjoy each other.
Thanks
Jana :D :) ;)