If you can share pictures or descriptions of the markings, we can tell you its heritage. It should have commercial proof marks.
I have observed several Greener Lee Speed sporters and they do not all say "BSA Co." on the socket. Also, some Lee Speeds have a model designation, such as LE 1. There are quite a few variations of these things, and very few rules that don't have exceptions.
Any info you can share on this or any other Lee Speed would be a big help to my project and I will return the favor.
Thanks!
-------------------- Researching Lee Speeds and all commercial Lee Enfields. If you have data to share or questions, please send me a PM.