The factory ledgers for these numbers no longer exist, so I can't give you an "exact" build date (day / month / year) I'm afraid... But we can "accurately" calculate the month / year:
The BSA with frame number WM20.74120 was delivered under contract C/13290. This was a contract for 10.000 bikes (5000 RASC, 5000 RAOC). Frame numbers were #71818 - #81817. There were two blocks of census numbers: C4752401 - C4757400 and C4860801 - C4865800. The census number of your bike would have been C4754703. It was the 3303rd bike from this contract. Production started at the end of November 1942, @ 400 bikes per week (approximately). This means that your bike must have left the factory in February 1943.
This is a sister bike of your WM20:
This frame number is also in the post war KeyCards, which means that it was still in use by the British Army after the war. Its post war registration number was 06YE84. Lex can do you a nice hi-res scan of this KeyCard.
Here’s a “close” number:
The BSA with frame number WM20.101237 (and matching “duplicated frame number” on the engine) comes from contract S/2603, which was a contract for 8.000 motorcycles. Census numbers for this contract were C5207518 - C5215517. Your bike's census number would have been C5211937. Deliveries for this contract started mid March 1944, @ 2400 motorcycles per month. Your bike (or “your engine”…
must have been built in May 1944.
These are two "close" numbers:
email (option): wd.register@gmail.com