What I do know. Both Haddoke and Weiland give BSA short shrift in their books "The British Boxlock..." and "Vintage British Shotguns". However both do say the shotguns were manufactured from 1920 into the '30s, and that they represent solid dependable boxlock guns.
Wieland says there were three grades from the utilitarian blued framed un-engraved extractor version I have seen before to a mid grade extractor with some engraving and a top grade fully engraved with ejectors. The gun in question seems to be the third variation...Geo