The National Childbirth Trust has always been quite active in Kennington - as much because there is not a lot around. (It sort of overlaps between the Lambeth and Southwark or of the Clapham Branch depending on which way you feel.) There are always a few people from SE1 who are interested but not enough always to form critical mass. And people tend to move out once babies are born - or go back to work.
It is a way of finding out about classes and meeting people with new babies, and the nearly new sales are good. The magazine will have lots of adds for things like yoga, though much in Dulwich. If you want to contact me directly I could give you the name of my friend who runs the post-natal support for Kennington and may know where things are in SE1.
Coin Street runs something called Family Links, run by someone called Natalie Bell. I am pretty sure it is supposed to be for the wider SE1 area - you could contact Natalie via Coin Street.
SE1 is not a particularly family area, but my experience has been that this causes people to make more effort and that this pays off in the end.
Jos - I have not found any non-smoking bars but The Leathermarket is a good pub when you are pregnant (and when you are not !) as it is spacious and airy and so doesn't get smoky, at least not when I have been there. I vaguely remember hearing that Tas restaurants may have non-smoking areas but I could be wrong - they are definately child-friendly though, for after the Event, I have taken a 6 month baby there at lunchtime and he was made very welcome. At Tas Pide I have seen someone on a Friday night with a very small baby and no-one seemed in the least bit bothered.
Topnotch gym at London Bridge supposedly has a trainer who knows about pre and post natal exercise, though I have never tried the service out and am currently not too happy with them as they will not give a concessionary membership rate for people on maternity leave - £500/year is a huge amount of money when you are living off statutory maternity pay.
Sarah - I would be interested in contacting your friend in NCT, I will try to contact you directly. When I had my first baby 2 years ago I also found SE1 to be a difficult place re. things to do, especially as a non-car driver as all the good things seem to be in Dulwich, Greenwich or Battersea ! With No. 2 due in May I am hoping to get more organised and find some like-minded people out there.... otherwise I may go up the wall !
I have a 6-month old baby and can mostly give you tips on being with a baby in SE1.
I like the Tate Modern (especially member's room if you are a member) and Southwark Cathedral cafe: easy-going places where you do not feel utterly out of place. Tas Restaurant is indeed child-friendly. The Bermondsey on Bermondsey Street has also been a safe haven. Avoid Fish! restaurant: they have no concept of what one needs when out with a baby and they are definitely NOT smoke-free, despite what they might say.
There is a Yoga/Pilates place in Bermondsey Street (but expensive). Otherwise get in touch with Charterhouse-in-Southwark, on Tabbard Street. They run Pilates classes a very reasonable prices. Otherwise I am still to find a swimming-pool with a creche (I carry on dreaming...) or a parent & baby club within walking distance.
Please get back to me on any other ideas you may have, it looks like there are enough of us to start a club!