Remember seeing an old war office newspaper advertisement, requesting the loan of .177 air rifles for the duration of the war, that listed the various patterns they required. I think that was WW2 era, but not positive. There was also the New Zealand tank training barrel inserts. Webley Junior air rifles were used for training in jungle warfare schools in Malaya in the 50's.
I wonder what year the pellets were procured ? - Have heard of Bsa underlevers used for LDV and Home Guard training in village halls. Would imagine quite a lot of that would have gone on on a semi official basis.
Perhaps they used commercial pellet tins/boxes, like the post war cadet forces - as you think some of the packaging would have survived.
You don't see any regimental airgun shooting shields either - which you might suspect to come across if it was an official thing.