Hi,
We live just off Wandsworth Common and both our children 3 and one and a half year old go to Second Steps in Ravenslea Road. It is a fantastic nursery, privately owned and my children have been going there since they were both one. Funnily enough I started my eldest at Kids unlimited when we lived near there and didn't really rate it as it is a big chain with lots of temporary staff. Second Steps is really lovely. Very nurturing and they take the children swimming and on trips and hardly ever have temporary staff. Good luck.