Hi Russlad, welcome to OpenStreetMap! Just because a path is on private property or impassable doesn't mean they shouldn't be mapped. These are both Public Rights of Way (PRoW) and are clearly signed as such (visible on Bing Streetside) so anything preventing access here should be reported to the Council.

As for all the other highways you have deleted in your other changesets, there are methods of indicating private access (e.g. https://wiki.openstreetmap.org/wiki/Tag:access%3Dprivate )

What happened to Puzzle Woods?