From the "L" prefix and finish its possibly a 1940 BSA No1 MkIII, just on the cusp of the changeover from when they stopped making "proper" MkIII rifles and started making Dispersals. That could explain why the date might have been omitted - later it was the "SA & Co" that was deleted, leaving just the "B".

It looks like its been rebuilt as someone's project however - Ishapore wood, as bigduke6 mentions.