The problem with deleting these instead of using appropriate access tags is that they're visible on aerial imagery and likely to be re-added without any access restrictions or other information.

If you have a desire line path which is visible on aerial imagery on National Trust land where you are, as the landowner, in a position to forbid access, you'd be better off using either access tags, e.g.:

highway=path
access=no
informal=yes
note=*

... or lifecycle tags, e.g.

disused:highway=path
note=*

You can use the note=* tag to include a short description of why NT would like people to stop using it.

osm.wiki/Why_can%27t_I_delete_this_trail%3F