Hi Matt,
I think you might have a problem tracing this one. The DVLA records show that it was indeed manufactured in 1958 but was registered with PSY 367 on 9th. September 1996. I suspect that the original registration number was sold and the bike now sports an age related number. Without finding the original logbook and matching it up with your frame number I don't know of any other way of finding the original registration number.
Finding the original documentation would be a bonus but without the registration number you would have to rely on photographs either in the motorcycle press or on these bulletin boards, hope that somebody recognises the bike from years ago and actually remembers the original registration number.
The BSA Owners Club also might be able to help by putting a photograph in their monthly magazine and appealing to their members for information. Long shots I know....but could be worth the effort.
Good luck with your quest,
Beezageezauk