According to the KeyCards the bike with frame number 111576 was registered 71YC94 in 1949 (when the old census numbers were replaced by the new VRM numbering sequence). It demobbed in February 1970. With a service life of 25 years it is logical that this bike went through a REME rebuild. Are there any data plates on this BSA indicating such a rebuild? (https://hmvf.co.uk/topic/46047-the-rebuild-identification-thread/). During these REME rebuilds frames and engines almost always got mixed up. The bike with frame number (and duplicated frame number on the engine) 116651 is one of the last bikes from contract S/5209. It would have had census number C5557351.
Here's a photograph that was taken at the BSA factory, during the contract S/5209. This is how your bike would have looked like when new.
Thank you all for the links and information. We are making headway into the history. I asked the owner if there were rebuild plates and he said no. The only other marking he found were these stamps. Do these mean anything to anyone?
As mentioned above the C number was C5552276, as shown on Key Card 28a, a full scan of the card is available from me, for 20 euro's, there are appx. 17 bikes on one card.