Yes, that's right, Themas.
Hardy49 - did you not post about this a few weeks ago? I'm afraid if you have now found out that no-one actually owns it, there's not much more you can do. As a right of way, the local authority has the obligation to maintain it and 'owns' the surface of it, but not the land underneath it.
If it is bridleway it is for foot and horses only and could be limited to 2 metres wide only (the minimum width for a bridleway). But whether you can persuade the local authority to put bollards up at the ends to prevent motor vehicles getting down there is another matter. Try Highways and see what they say.