Here's what I found: "By the late 1930s the need for new rifles grew, and the Rifle, No. 4 Mk I was first issued in 1939 but not officially adopted until 1941." The citation for this is:
Skennertonicon (1994, 2), p.5
I got it from wikipedia...I know a lot of people say that it is not reliable, but if that info really comes from Skennerton's book I would assume it is accurate. Does anyone have that book to reference it?
Lee-Enfield - Wikipedia, the free encyclopedia
under Rifle no. 4, first sentence.