I've tagged it as suspected:designation=public_footpath according to https://wiki.openstreetmap.org/wiki/Access_provisions_in_the_United_Kingdom#Public_Rights_of_Way 

Checked with public OS data (specifically the "Public Rights of Way" layer in JOSM). We cannot use "the OS map" as a source, but certain OS data releases under OGL are free to use.

That's a start. Really, this entire path North of here to Church Hanborough needs checking on the ground in order to determine its proper RoW designation.