If it's a BSA you have I can supply you with a C number but I need your frame and engine numbers to find out. Depending on when it was build it can have the C number in a few different locations.
From memory, my chassis number is 110717 which would mean your bike was only 139 behind mine. My census number is C5551417 so, if I'm correct, yours would be C5551556?
Lee is correct with your tank number, I'll send you some war time photos of BSA's with tank numbers close to yours by email.
Your BSA would have had the tank C numbers on both sides of the tank. Your engine number is very likely a replacement engine from during it's military use, we have lists with lots of strange numbers and no knowledge about the meaning of them. Originally your BSA would have had matching engine and frame numbers.