If your 4T is dated 1933 then it can have only one manufacturer; RSAF Enfield, the 'home' of the Lee Enfield. It sounds like you have a very rare & desirable Trials rifle, made at Enfield & then converted to sniper configuration there in 1941 (or possibly, in 1942). If you can get us some photo's we can hopefully confirm this for you & possibly give you some more information about it.
The scope it bore, incidentally, was a No32 Mk1, serial number 3238, made by the Houghton Butcher Manufacturing Company of London, in 1941.
Can you post us a few pics?