If it is an Imperial, it seems to be a vastly customised one Deejay: the drum clutch as well as the engine, engine clutch, and handlebars seem entirely unrelated to normal Imperial parts. However I can't imagine an English mower having a Kirby Lauson engine, or an engine deck height that would suit one, either. How about one of the slightly obscure Australian reel mowers from the 1960s-70s?
Anyway, we still need to get the drum sprocket off. If it isn't an Imperial, and since it has a drum clutch, it doesn't make sense to expect it to attach directly to the drum axle. We need some more pictures of the detail of the sprocket's hub, and/or an actual identification of the mower so we can try to find a manual.
Does the sprocket rotate freely on its own bearing, or is it rigidly attached to the drum? I can't visualise it directly driving the drum, since it has a clutch mounted on it.