There is a good riding school in Dulwich called Dulwich Riding School. Mixed comments about it I have read but it depends on what you want. Dulwich has produced some fantastic riders over the years I have been riding with them for quite a long time. Dane Rawlins Director of Hickstead and renowned British Dressage coach rode with Dulwich and many more. If you just want to get on a horse and hack out and just have fun I agree probably not the best choice, but if you are serious about learning and want some fun too then it is a good stables. Rides in the park are limited but can be a nice change from the school when you have worked hard, what I personally do is have five lessons in the school and then book a hack at stable that Dulwich has recommended for a hack with more hacking facilities, this way I get the best of both worlds. My confidence has grown my ability has helped me pass my British Horse Society Exams overule been a good choice for me. Best thing to do is go down and have a look around you can then make up your own minds