Pre. which war ? I probably have an AW from 1938 -ish or a late 1920's K type both with control levers.
Lots of Roadsters left the factory as single speed models and had a Sturmey added later as funds allowed or the bike changed hands so personally I would fit any 40h hub.Post 1946 hubs can be picked up very cheaply.
This site is a good source of parts( as well as E-bay of course.)
