Well, I can be somewhere for 1pm. I will try to come up with some suggestions, though we have:
Eddie Catz in Putney
Kew Gardens
Richmond Park
I was being flippant when I said Wandsworth Common, but if it does work for anyone, add it on by all means. It has an overland station, I think from Clapham Junction/Victoria.
I think the weather just isn't reliable enough so will investigate some soft play places further SW. Infact, I will do that now.