Hello Andrew Saunders, and welcome to OSM.
I'm a bit surprised that this path is not signed as closed in any way, given that there was a previous discussion over at https://www.openstreetmap.org/changeset/135290950 where some National Trust people said that they were trying to close it.  You wouldn't happen to have taken any photos while you were there recently?  I've asked the same question over on the NT changeset.
Best Regards,
Andy
