Ask me next week, then I can access my files again, and check the Key Cards.
Can strongly recommend the excellent "British Forces Motorcycles" book, make sure you have the latest edition, there is the most current info in there.
The BSA with frame number (and duplicated frame number on the engine) WM20.112853 was built under military contract S/5209. This was a contract for 12.000 bikes (frame numbers 104818 - 116817). Unfortunately the late war factory ledgers no longer exist, but we know from the Receipt Cards that BSA started delivering this contract in early September 1944, at 2.000 bikes per month. This means that your bike must have left te factory in December 1944 or January '45. The military census number would have been a rather nice number: C5553553. I've added a picture of the BSA assembly line, with bikes from the same contract (same specification). A lot of contract S/5209 bikes were transferred to the post war Dutch Army.