There is a new baby swimming pool in Wandsworth, London Baby Swim,
http://www.londonbabyswim.co.uk/?gclid= ... tAod7RYAJA
but I believe it's booked up until at least July now.
I've been taking my 3.5 month old there (we've had 4 lessons) and so far we're very happy with it. It's specifically for babies and toddlers, low chlorine, lots of baby changing mats, etc