Same here - fished them from about 1978-1985. Tench fishing mostly in Home Park (the Hampton Court side) and in Diana Pond in Bushy Park which was crammed with tench in the 1-3Ib range plus a few large carp by the statue, then there was bream and some better tench in Heron, and lots of easy carp in the Leg of Mutton Pond. Last I heard virtually all the ponds were carp focussed with some big fish (30s) in several of them - but highly pressured. Diana Pond has recently been drained (a couple of years back) to restore the statue in shiny gold leaf and all the fish were removed. Now it has refilled i understand there is still no fishing on it and no idea if any got put back.
Most of the ponds are very busy, especially during school holidays or in dog-walking weather. The Home Park ones are harder to get to without a long walk so are quieter. I miss the place, it was where i learnt a lot, and the surroundings can be spectacular.