1930's Rudge. I'm not an expert, but I believe this is a Special. If the tank is original then it's likely to be early thirties - you can just see the marks where the original hand gearchange has been removed on conversion to foot change. The "Brooklands Can" style silencers are also typical of the late twenties and early thirties. Despite its gleaming condition, it was ridden some distance to this show, not trailered.

UPDATE: I'm fairly sure this is the bike mentioned in the Autumn 98 issue of 'The Radial', the journal of the Rudge Enthusiast's Club. If so, it's a 1930 Special, and was once owned by Mike Hailwood. I believe it has now been converted back to hand-change. I bump into it and its owner occasionally - I'll try to get a more recent photo.