There were many variants of Albion boxes! This is the 2-speed + clutch variant. In the 1931 catalogue for "Albion Midget Gear Boxes" this model (identical?) was referred to as the BJ. I know nothing, but maybe BF was an earlier model, say 1927?? In 1931 the EJ gave 3 speeds + clutch + ks.
Anyway, no reason it couldn't go into a bike from the 1920s, although Australian made stuff (for example, I'm thinking Waratah) tended to offer 2-speed no-clutch for a base model, or fancy 3-speed + clutch + ks. Although by 1927 maybe even the basic 2-speeder needed a clutch.
Also, chain final drive was taking over from belt around 1927.
Leon