Not too many people here like the quality of the repro scopes. Really interesting though, that you have the original shipping box and provenance. The No4 Mk1 (T) folks here will be on this by morning, What a find!
Here's a link to a similar BSA No4 (T) discussed on this forum: https://www.milsurps.com/showthread.php?t=48931
Salt Flat