From my understanding, you can't take off from NT land, but there's nothing stopping you from flying over their land as they don't own the airspace above it. As there is a public footpath running down to the worm's head there's nothing stopping you taking off from there and flying over the beach and to the worm as I did. The law states that while "a public right of way protects you from being accused of trespass it does not protect you against any by-laws. And since the National Trust by-laws have not been updated since 1965 and make no mention of drones, unsurprisingly, I think i'm in the clear.
The general consensus seems to be that the NT don't have much of a legal leg to stand on so i'm not going to worry to much about it.