Yep spot on. I lived in Bucks in a private road established from 1911. This was really unadopted by the council & before we left I was the chairman of the frontagers associtaion who maintained the private bit . We paid to maintain it but the public could use it & it was a rat run to the local primary. We filled pot holes, marked speed bumps etc as per the law.
At the bottom of the road ( a 1/2 mile hill) were lots of potholes in the council bit. We paid to fill them in as we were doing the private bit only to be told off by the council. Go figure.