bob's suggestion seems good to me - the most distictive part in the photo (to me) is the front fender - there has got to be something about that particular front edge that only one bike maker did... it's not a smooth round arc, but seems to have more of elliptical bulge at the front and center, and i don't think the effect is caused merely by attenuation from the peculiarities of the lense or angle of the photograph. most cameras back then had fairly shallow depth of field and nothing like the distortion caused by a specialty lense such as a fisheye or extreme wide-angle.
i'd say that restored Sloper is decked out military style - blacked out, definitely not a stock bike like what your ole da was perched on...
the photograph itself was more than likely taken with a mass-produced "over-the-counter" camera with a fixed lense. that's why i can't shake the feeling that that front fender is in its design, distictive.
that makes .04 cents you have now...don't quit your day job, but keep trying - i'm sending this thread to my dad, born on date 1942, to see if he recognizes the image...he's an old BSA guy himself...
cbj...