This was my understanding, that as its a Royal Park it has some by-law that makes cyclists fair game for fines. I've just cycled around Battersea Park (not a Royal Park) and there are signs there saying its a 12 mph speed limit but this only applies to motor vehicles, and I've cyclist past many a copper at much faster than that and they don't bat an eyelid there.
Richmond is a different kettle of fish, I don't go to Richmond anymore as its full of cyclist nobbers riding like douchebags trying to beat PB's. A popular challenge across other forums is to try and do 3 laps in under an hour, which as 3 laps is about 20 miles it means averaging over 20 mph for the whole 3 laps, so there's literally 1000's of cyclists trying to beat this every day. The police hide with their ray gun at the bottom of Broomfield hill where it is very easy to do 40mph, but over the course of a lap there is only really 2 or 3 places where cyclists can easily exceed 20mph, and only briefly. I've seen numerous cyclists pulled over before but not once have I ever seen a motorist being fined, it just strikes me as a waste of police time. There are definitely more pressing things the police could be dealing with, but traffic seems to be seen as a cash cow these days, and the fines seem more to do with income generation than any concerns over safety.