As far as I am aware, Knibbs International retains all production records for the early Airsporters and BSAs, however, I may be wrong but believe there will be a fee charged by them for researching the records and providing you with the info you seek. Might be a good idea to contact them and seek information from them as to what kind of information they can provide you with, for example, will records confirm the production date, (ie, day/month/year) the dispatch date or whatever.

atb
ASM