Wacky kingdom Kingston

Should try the little borough in weybridge! It has a brilliant sensory room! And have slot of groups on for new mums, all ages actually!
I’d definitely recommend

I would recommend the little borough and munchkins. Wacky isn't for 4month old baby.

They do have an area aimed at younger kids but I'm not sure it would work for a 4 month old - it's aimed more at mobile kids.
You could try Picnic (also in Kingston - what had more of a baby area) or Little Bears play cafe in Hampton Hill.
Three Methodist Church in Teddington has a 'Tots' drop in session on Wednesday mornings (9.30 - 11) which is only £3. The play session is non-religious. A number of three v other churches and community centers in the area do similar things on different days/times. Worth checking those out as they are a lot cheaper.
Teddington also had a really good range of baby's sensory/yoga/dance classes of different types.

Soft Play at the Pod at the Hawker Centre in north Kingston has a great sensory room for babies (and good soft play for older kids too!)

Kingston town children’s centre do stay and plays as well as things like baby massage. Picnic has a baby area and is cheap at that age. The curzon cinema usually does baby cinema on Fridays. Also have a look at hello Kingston kids for classes and playgroups throughout the week too.

I just came across this free web app where you can add and review these places for next time and for the next mum! I started adding them for Malmö but it looks like it’s worldwide!https://www.babyccino.app