Hi Jon,
I looked at the photos before I read your post, and I thought it looked like a "cooking" BSA single, just post war. So, yes, a B31 (350) or B33 (500). In the photo with the Douglas you see - through the spokes in the Douglas front wheel - the push rod tunnel, which pretty-much confirms BSA. Plus the fork, brake, etc.
Love the ring of fire photo!
Cheers
Leon