BSA military patterns were given / bought by British regiments or cadet schools, some were marked as per;
https://www.flickr.com/photos/312284...7627403551588/
https://www.flickr.com/photos/312284...7627403551588/
Granted these are more "property of" rather than the broad arrow type where guns have been evaluated by the board etc.
I think BSA were hoping for the latter and the ones they gave away or sold at a discount were used in their adverts to try and get sales. (as used by several regiments etc.).
ATB, Ed