Dale,

I was looking for all and any signs. The public footpath signs were pointing along the PRoW as expected, but the track leading to Hill Farm & Hill Farm Cottage had no signs at all from either end.
If you are the land owner of the track between the two PRoW and say that there is no public access that is enough to make it as access=private on the map.
OSM works on mapping what is on the ground, or if something is explicitly stated (i.e the route of a PRoW, even if there is nothing on the ground). For this reason normally we require some signage signs dictate what the access to a way is. I've amended the track to have access=private which on the normal OSM layer will render as a gray dashed line (although it can take some time for the changes to appear on the map)