Hi, welcome to East Dulwich! Take a look at St Mary's in Nunhead. I'm a SAHM in East Dulwich too. I have a 3yr old and 1yr old and like you wanted somewhere my eldest could go for some independent play for a couple of hrs in the morning, without a huge waiting list. My 3yr old has been going to St Mary's since January and I think it's great. They only take children from 2 upwards and it's very play focussed and the ladies there do some lovely things with the kids eg baking, arts and crafts, visiting nursing home nearby. Feel free to PM me if you have any questions.