http://www.bsaownersclub.co.uk/Engine_Frame_Listing.html has engine and frame number info. It looks like your engine number starts with CA10R ? In which case CA10R was used for years 1954 to 1959 and your number is in the 8000's so would be from a 1959 Super Rocket, the cylinder head on the bike looks like alloy not iron which would also confirm it is one of the sporting models engines.
A 1959 frame number would begin FA7....
It is often not easy to decide what bike you have, as parts get swapped about over the years but a good start is to find out what frame you have, and go from there. The bsa club and vintage motorcycle club in the UK have the factory despatch records and tell you what year a frame or engine was despatched and what the bike specification was, oddly the records are in engine number order so it is hard for them to date a frame when the engine number is not "matched", or if you don't have an engine number, as they have to search through hundred of records looking for the frame number.
It is quite rare for a frame and crank cases to stay together all of a bikes life, if they do then you have a "matched numbers" bike (even though the numbers are actually different) which is nice but doesn't make it go better!