Dont forget Corams fields (http://www.londonkidz.co.uk/Homepage.php?keyid=517) in London. Catch the tube to Russell Square, turn right as you come out the tube station and follow the road down past Brunswick square, over the round a bout, round past International House and then bear left. The gate is about 100m further on. I never went in there, but lived in the residences on the other side of the fields, and was always hearing kids laughing and squealing. I know there are peacocks and some sheep there, along with climbing frames and stuff.

Also beware the park has a strict policy that adults and over sixteens can only be admitted if accompanied by a child.

In Singapore - Cant actually think at the moment. The Botanical gardens are always good, but if you are there during Moon Festival the Chinese Gardens will have a huge area devoted to kids and laterns and things.