Frame number WM20.76381 is a contract C/13290 bike (10.000 bikes; frame numbers 71818 - 81817). The original census number would have been C4756964. Production for this contract started at the end of November 1942, and during this period BSA produced approximately 2.000 bikes per month. Which makes me think that your bike must have left the factory in February 1943. Here's an early bike from the same contract, photographed in Normandy in 1944.
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Jan, the motor in the bike is WM20, 95045 with RW stamped below the serial number.
I have a spare motor, 100484
The bike with (duplicated) frame number WM20.95045 would have had census number C5128445. It was built under contract number S/1048, a contract for 15.000 bikes (census numbers C5115218 - C5130217). Production of this contract started in June 1943, at 2.000 bikes per month. Which means that number WM20.95045 must have left the factory around December 1943 - January 1944. Here's a picture with a "close" number:
The bike with (duplicated) frame number WM20.100484 would have had census number C5211184. It was built under contract number S/2603, a contract for 8.000 bikes (census numbers C5207518 - C5215517). Production of this contract started in March 1944, at 2.400 bikes per month. Which means that number WM20.100484 must have left the factory around May 1944. Here's a picture with a "close" number:
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