[400ixl]

Unadopted and private are two different things.

Unadopted means the local authority have now responsibility.

Private means the land is owned by an individual, company or consortium of individuals and is registered as such with the land registry.

It can be unadopted and public if the registered owner is not known and registered. Often the frontage owners jointly maintain these types of roads. But they aren't private as such.

First step is who is the land registered too.