These are 1" Aiming rifle cases.
These were made by Birmingham Metals and Munitions ("B") and the "IV" is for the Mark IV version of the cartridge.
"M" is for the Morris version of the electric primer as opposed to the "KN" (Kings Norton) type.
I have a trench art pair of these, just like yours. I guess they must have been a popular thing to knock up, maybe due to their small, handy size?