These streets are not access=private, as this would imply a fully private gated community, which isn't the case here. That would only work if there were a staffed gatehouse, which is somewhat improbable for social housing built in the 1920s.

Setting this blocks pedestrian access, which is incorrect. There are consumers of OSM data for routing other than Amazon's deliver drivers.

I also do not believe that delivery vehicles, taxis and the vehicles of other visitors are excluded from the estate roads.

More appropriate tagging might be access=destination + ownership=private.

Reverted in https://www.openstreetmap.org/changeset/162156017