Wot dave said.
Its was the now deceased Earl of Scarborough who was concerned about liability issues. It is also an SSSI so tread carefully and don't litter.
The heir to the title is a lot younger, and as far as I'm aware hasn't expressed any opinion either way (my friend works on the estate and lives above the National Trust gate house to the abbey itself, if you get asked to move on it'll likely be by him, but he's a nice guy and used to dabble in climbing himself whenever I dragged him out).