Re:
The frame is a BSA Prima, 531 Reynolds (unless the sticker is incorrect) from whjat the previous owner said the bike is circa late 70s early 80s whcih seems to match up with the information knocking around online.
Unfortunately the frame is very slightly on the small side, at 6 foot 8, beggars can't be choosers, especially with a free bike. The shifters were clamp on as you say, hence the slightly redder areas where they previously sat.
How do you mean the fork is not right?
I have not looked for any numbers on the BB, why do you ask?