We've just done NCT classes which were based at St George's church in Borough; they're a bit costly though but they are a good way to meet other new parents which can be very important when you're on maternity leave. Your local GP practice should also run antenatal classes which are free (NHS) and cover all the baby basics.
We did a course with NCT and you can check their website for forthcoming courses by postcode, but also check with your GP and the hospital you're assigned to for the birth. There was a rolling programme of classes at both our doctor's surgery at our hospital. They were during the day so difficult if you're working a 9-5 until the birth as we were, but they are free so a big saving vs NCT. Hope that helps!
Also check Southwark website. They (at least used to) offer several classes, both ante and post natal. Some (but not all) of them were advertised in our doctors, so it was worth checking on the Southwark website.
(Disclaimer - my experience of this was 6 years ago).