It sounds just like my No.4T and I KNOW that mine is bitsa. That is say, I have a 1945 BSA with a Roger Payneicon repro bracket and a No.32 Mk1 - which is wrong for the year of the rifle.

I'll wait for the "fount of all knowledge" on this stuff to confirm but I just can't believe that REME would swap a No.32 MK.3 for Mk.1.