Have you tried searching on the Trailwise map tool?
http://www.trailwise.org.uk/gmaps/gmap.htmgo to the area you want by panning and zooming, then press the button bottom right, then again on the button that appears above the original. Hover over the lanes that appear (if any) and click to see the names and authorised users, the road name is displayed as well, but this may not match the ones on the posted signs.
The definitive map for that area may be a better option if the council has an online version.