There are other interesting details in your photo.
Look at most photos of WD bikes and they have a standard blackout mask fitted to the head light. The ID number is painted on the tank (no number plates) They are painted standard forces colours, khaki, desert, RAF blue etc.
Your Grandads bike is quite different. It looks like a normal civilian model as if it may be one of the civilian models impressed by the forces in the early days of the war before wartime production really got going.
An old boy I knew years ago told me about policemen standing by the side of the road stopping motorcyclists and taking their bike right then and there if deemed suitable for war use. For that reason he always rode a two-stroke because they never took anything two-stroke.
To finish off, yes, Ariel.