There's loads of parks for free.Does Battersea Park still have the little zoo?Going back about 10 years but we used to love that and it was much cheaper than London Zoo.
There's a little park near Great Ormond Street Hospital called Coram's Fields if it's still there.You're only allowed in with a child.It used to have animals,play equipment.
There's a toy museum,near Kensington Gardens,not sure exactly where.We used to love Richmond Prk,massive green space if you're stuck in the city and need a bit of air(quite a way out though,think you can do it on a bus).Lots of city farms.Of course there's the palace,the changing of the guard,St James's Park's right there too.You don't have to spend a lot,depends what you're looking for,and if you're brave enough to do the underground with kids in tow(I used it regularly with toddlers and a double buggy)