Hi Matt,
Welcome to the Forum and classic bike ownership (for which there is no known cure, once the bug bites, that's it!!!).
I'm afraid I don't know the bike, tracing history is often difficult.. The DVLA may be able to help, as might an ad in something like Old Bike Mart or internet magazine ads.. Either way it's a long shot, but I wish you luck.
You can check details of whether the year of your bike is correct (and whether the engine and frame left the factory at roughly the same time!!) via:-
http://www.british-only.com/pdf/framenumbers/BSAengineandframenumbers.pdfYou've come to the right place for help though - the Forum has been absolutely invaluable to me, I'm sure you will find the same..
All the best,
Adrian