Hi.....I really don't know personally....The earliest reference I have found for BSA Branded pellets is dated 1908 and refers to the Adder pellet, and even then they were recommended as the ones to use exclusively above any other brand, both because BSA could guarantee the quality of the Ammo...and obviously they didn't want to lose pellet sales to other makes...I believe they were made at the rolling mill at Adderley park (BSA bought this in 1873)...These later were then were branded just BSA, but the pack and pellet design seem to be the same...(in fact doing at bit of research, these later pellets below were made by Cox and Co. of Lozells, Birmingham)
http://www.flickr.com/photos/3122848...7607964699940/
"Witton" pellets, (made by Kynock).the forerunners of the Wasp and Pylarm types, came after, but these were not marked BSA, only recommended by BSA I believe, so do these count?
After that, the next one I personally am aware of is the Pylarm pellet, which arrived in the very late 1920's / early 1930's....A long running pellet and contemporary to the Eley/Kynock/ICI Wasp brand, the earliest tins were paper labels on top,with a gumstrip sealing band;
http://www.flickr.com/photos/3122848...7607964699940/
They progressed (as screen/litho printing became the norm) as did the wasps, till in the late 40's / early 50's the tins had the same graphic design, but looked more "modern";
http://www.flickr.com/photos/3122848...7607964699940/
At all times BSA had a strong brand/export creed, and very well established dealers and marketing in all the emerging export destinations, so I can't see why they would let someone else manufacture stuff for them (at that period) without being really fussy about the quality etc..Plus the area around Birmingham (and Eley London) had the most modern plants for pellet production...the later BSA pellets may well have been Eley / Kynock made....I don't know that either!...I have seen old tins of with "made for use in BSA" etc.... ie; Beatall by lanes which Have "recommended for BSA rifles " on the tin, (which I am suprised BSA allowed!) But nothing with "made for / under licence from / BSA"......remember, in the 1920's /30's BSA guns were pretty much still the most sought after and respected design...even the Germans were copying the basic layout and look, so anything say a pellet maker could do to try and associate themselves with BSA would probably improve their sales.....This is not to say that they did not do as you asked, the simple and short answer (I can never do these)..
Is....I personally have never seen/read/heard anything along these lines, but would be interested to hear any info you may have uncovered ...as it is all a bit like tracing your family tree trying to work out the history of some of these little lead fellas