lakedistrict
I spoke to someone who recently tried driving down here, and I've now changed the road to a track roughly at the point where they described it as such. The wiki suggests that the track tag is used in such case even where the road is a public unclassified one: https://wiki.openstreetmap.org/wiki/Roads_in_the_United_Kingdom#Unpaved_country_roads 

I'll leave it to other mappers and future users to add further details such as surface/width/tracktype tags (Street Complete may ask for these). 

As it is signed as a no-through road from the north end, it seems fair to say that motor vehicle access is officially discouraged, so I've tagged that on a node. 

https://www.openstreetmap.org/changeset/145014558