Shepperton is brilliant and not too far from Tooting. Open on weekend mornings, Monday and Wednesday evenings as well as Wednesday morning!
Here's their web site: http://www.sheppertonopenwaterswim.co.uk/
Get a train to Shepperton and it's either a shot walk or a quicker cycle! They also hire wet suits if you forget / don't take your own!
£5 a session, nice beach to walk in, friendly helpful staff and a warm shower afterwards at the next door sailing club! Tea and coffee are available, just no bacon butties!!