Well this thread has caused fun!
Just as Noel says, and Duncan, the position of the exhaust and carb makes it a four stroke and the shallow head says side valve. The poor image makes it impossible to see the side valve chest cover that should sit just below the barrel, presumably it has been painted black.
This first image is of a 1940 BSA M20, side vale single, but the cover for the magneto chain is not quite the right shape.
This second image is of a 1951 BSA C10, side valve single, and the chain cover is the right shape. Obviously this 1951 model has telescopic forks but a BSA marque expert would have to say whether this engine first came out in a rigid frame with girder forks a few years earlier.
Edit: yes, found C10s going back to 1939 link
Previous identification by Micheal and JohnF acknowledged.
Edited By norm norton on 25/01/2022 10:34:10