"Private Road" signs on an un-gated road do not mean private access, they mean that the road is not publicly maintained and that there is no right of way. In OSM, this is tagged with ownership=private. For roads signed "no through road", access=destination can be added. If through traffic is allowed, access=permissive is used.

Residents at the far end of Woodland Way would probably prefer it if deliveries, taxis and visitors can navigate beyond the junction with Higher Drive.

Updated in https://www.openstreetmap.org/changeset/165579462