G'day Murray,
Welcome to the forum.
I'm in Melbourne also, Nice find. If you scroll up and click on the forum photo it takes you to the M20 web site, click on Civilian M20 then the what year tab. X denotes post war 1945-47 but for M21 it's 1946-47. 3073 seems like a low number so I'd say '46.
Nice to find you have an extra 100cc's how ever this is only equates to about 2 hp.
Looking at Model Recognition Points it doesn't look like they changed very much 39 to 46. I'm not sure where the claim of 1939 for this machine comes from but I may learn something when I get the paper work.
I'm afraid that I can't tell you anything at all about your post war engine Murray... The frame on the other hand is definitely military. The BSA with frame number (and also duplicated frame number on the engine) WM20.45171 was despatched from the Birmingham factory on 15/9/41, destination Ministry of Supply, London. It was part of contract C/9310. This was a contract for 9.000 bikes (frame numbers 44213 - 53212). The census number on the tank would have been C4554680.
The bike was transferred to the Australian Army, where it received the AMF census number 9411. After demob it was apparently sold to "Page Cycles Motors".
Thanks Jan, that was way more information than I was expecting.
So I guess its the frame that sets the date. I'll call it a 1941 model then.
I found 'Pages Motor and Cycle Works' in Townsville in 1913. Perhaps they were still around two world wars later.