I fished Duddingston a fair bit when I was a lad. Loads of perch and your right Cumbrian all the kids fished from a big rocky outcrop. Never caught a carp but I saw them often enough, never caught or heard of anyone catching pike (Dunsapie was the place for them) but did catch the odd trout and am aware of at least one fish that was around 5lbs.
The Braid burn, where it runs through the golf course, is like a wee chalk stream, plenty of willing brownies in it, some of them surprisingly decent
Norm