Well, since no one else has responded so far, I'll give it a shot: it's probably an engine made for the Daytona race event ca. 1954. I have no proof of this, although I've been looking. My reasoning is as follows:
BSA Gold Stars set up for Daytona were frame-numbered CB32D and their engines were BB34GSD, for the 1954 event only. This was done to satisfy AMA Class "C" rules which required that a minimum number of any motorcycle model raced under AMA auspices had to be offered to the general public for sale. This number was, I believe, fifty or a hundred. The purpose of this rule goes back to the Great Depression Thirties when local racers were uncompetitive because high-priced factory riders and exotic, 4-valve whiz bang bikes (Harleys and Indians) were being used to strictly promote sales; inasmuch as "all politics is local", spectators lost interest, unable to see their local riders contend on equal footing. AMA created Class "C" to eliminate this problem. In fact, Class "C" events were "claiming races" (for a while) wherein anyone with the minimum fee could buy the winning bike; as you can imagine, this helped to keep the factories honest.
Anyway, you might have the engine (or at least the cases) from one of these Daytona engines.
I'll sit back now and watch the fur fly.
David