I'd be a tad more convinced about the Peak Park Authority's view of cycling if they hadn't erected signs along the trails specifically telling cyclists that they have to give way to everyone who isn't on a bike. Of course, the non-cyclists see this as their permission to be difficult with cyclists. Loose dogs, children, groups from the paramilitary wing of the ramblers etc. seem to be ok, but we are there somehow only if we don't get in anyone's way.
I'm not suggesting hooligan behaviour, but if another dog tries to knock me off, only for its owner to ask me why I didn't ring my bell and wait whilst they captured it, I might lose some of my cool.