The access tagging on this lane/drive looks completely wrong. I presume the drive up to the residential area is a public footpath and the footway leading S/SE is also a public FP?

Assuming it is otherwise a private road and no other permission is granted (horse / bicycle etc.) then correct tagging would be
access=private + foot=yes (on the public FP section)
It's also a good idea to add
designation=public_footpath
on the sections that are public FPs.
 
The track heading NE is also tagged with "access=permissive", which seems unlikely.
 