I wish I could take more credit, but all I did was post that message, actually.
I wouldn't be keen on re-opening the toilets as they tend to attract drug users, homeless people, etc and there are toilets not far away in the Horniman Museum.
I didn't know that there used to be a paddling pool there. That explains the concrete circle, I suppose. I guess the problem with a paddling pool is more the risk a child drowning in it (and from the council's perspective, them being sued).
I'm more of a dog hater than a dog lover, but if it helps to keep the dog free zones (inc. the Horniman Gardens) clear of dogs and dog poop, then I might be in favour of a fenced off dog zone.