[QUOTE=rebeginner;7654703]
I’ll be in London for a couple of days this fall, and found a thread somewhere here on COTH that lead me to Hyde Park Stables. I’ve booked a reservation, and do plan to bring my own boots and half-chaps (I’ll use one of their helmets, since packing mine is kind a of a PITA). I’m a competent amateur dressage rider (shown up to 4th Level), and have done some low-level eventing.
Am I correct to assume that if I can demonstrate a sufficient degree of aptitude, I will be allowed to actually ride out in the Park?[/QUOTE]
I did this years ago (about 2000). It was fantastic. Both my friend and I were riders (or had been, lol) and once they determined that we knew what we were doing, they more or less set us free. It was pretty awesome to be a hoyden and have a gallop on Rotten Row. 
Like I said, it has been a while, but if memory serves, you can’t just ride the whole park at will, but you have discretion about where you go in the areas where riding is permitted. It isn’t like many American trail rides where you are more or less on a plodding line of horses.