NT own large sections of the UK coastline,Dorset etc, and other large areas of land with no property on it. These places are little used by the public and most people are unaware that NT owns so much land.Just look at an OS map and you will see how much they own.
If there are no people about then I fly on these coastlines etc. I have only once been asked to stop by a warden who appeared from nowhere.
I agree NT do not own the airspace, but they do own the land and can prevent you from taking off and landing. A useful fact for coastlines is that the land below high water mark is usually Crown land, and you can legally take off and land here.
It may be that you can fly from a public footpath, but legally a public footpath only grants the right of passage and nothing else.