Many public highways in the UK have a private owner. That is, someone can prove "title" to them, either by being the registered owner or by having conveyances showing exactly how the land has been bought and sold over a long period of time. Such ownership in no way affects the public highway rights, since the relevant "highway authority" (usually a local authority or the Highways Agency in England and Wales, or Amey Highways in Scotland) is deemed to own the surface of the highway, despite someone else's ownership of the land it passes over or under.
