Have been back for a further look into this and to view a couple of more recent maps, Wayfinder appears to be out of date on this one and also doesn't name as much of Ox Drove as such as actually is (if that makes sense). EDIT ben back on and updated some of the info.
All but
one section on the eastern end appears to have been upgraded to BOAT so is good to drive assuming there are no TRO's etc in force. Having looked at the maps and Wilts CC site, you've got so many lanes to drive down there, 815km of BOAT in Wiltshire alone, we ought to have a weekend laning down there sometime.