Congratulations!
Here are some ideas:
Find out which is your nearest children's centre, ask for their program and see if anything interests you.
Hackney children's centres They are a good bet for free / cheap stuff.
I've not been but I've been meaning to get round to go to some kind of yoga type thing ...
Yoga home in Stokey have stuff for mums / babies, like baby music & movement on a Tuesday (birth - 4) and it's only £3 drop-in.
Yoga Place in Bethnal Green has been recommended to me. They say
"There are Baby Yoga Classes on Wednesday at 12.30pm, (from new born to crawling) followed by tea and cake at 1.30pm, where mums can catch up with each other."
I like the tea and cake idea It is quite pricey though, i think it;s about £10 a session.
The Rio cinema does a parent and baby screening every Tuesday and Thursday. Basically you are welcome to go with your baby, and as long as they are under 1, they let them in to a 15 cert (or whatever). The whole cinema is full of babies. It's great to be able still go to see a film, to BF without anyone batting an eyelid, and the babies don't make as much noise as you might think! I think it must be an interesting experience for them too - mine spent as much time looking around at the other babies as at the screen. Here's the programme Tickets £6 and £5 Concessions.
We did the Splashbabies programme in Kings Cross, but they also did it at the Sunstone women's gym in Stokey I think. We really enjoyed it. If you contact them they'll let you know when the next classes are. Again it's quite pricey though - I think it's £50 for 5 sessions.
Sorry most of those ideas cost money. I'll have another think ...