I don't let my daughter go in the dogs-designated area at the Horniman, and I never said that I would - the problem is that other, less responsible, people let their dogs poo and run in the other areas, particularly the grassy areas furthest away from the museum (I guess they think they won't be seen from there) which is a shame as that is just where children like to stretch their legs (toddlers need their reins-free exercise just like dogs do!)
There aren't that many local parks that I know of that don't allow dogs! Mayow Park, Blythe Hill and One Tree Hill are always full of dogs and dog poo. The Triangle is supposed to be dog-free but as others have pointed out this doesn't happen. If I saw some wardens around I'd love to report all the dog-mess I see, and the dog-owners not picking up poo. I've tried challenging owners about it, but the last time just got laughed at. There is simply no incentive to make the irresponsible dog-owners more responsible, and unfortunately this is something that Lewisham Council have to tackle.
As I've said before, this problem isn't just an inconvenience, and as much as we all love dogs we do have to bear in mind that this problem it is actually dangerous to humans.