Hello, there's a good one at Crook Log Leisure Centre in Bexleyheath at 7pm on a Thursday.
It's a council-run leisure centre so no need to be a member, or to register or book, you just turn up and pay (I think it's £5.25, and you need a quid for a locker). There's plenty of free parking as well. It's a really relaxing lovely class, not really exercise as such, more just stretching and relaxing in the water.
Might be a bit of a trek for you from Brockley though
Here's the address and postcode:
Crook Log leisure centre, Brampton Road, Bexleyheath, Kent United Kingdom,DA7 4HH.
It is about a 5 minute drive off the A2, so maybe not too bad if you have a car and can get onto the A2 easily, perhaps a Lewisham?