As the others have said, you have a nice BSA-made .310 Cadet rifle in great original condition. Yours has the better rear sight. Also have a look at the top of the chamber just in front of where the cartridge goes: You may see either one, two or three asterisk marks there.

These were stamped on the rifles when they were released for sale to the civilian market, and related to the bore and chamber condition. One asterisk means no corrosion seen, two asterisks indicate some chamber corrosion (like my rifle, which is not that bad) and three means more serious corrosion.

Your bore diameter will be 0.322" so do use the heel-based bullets. With a modest charge of red dot or similar these are accurate to 200 yards!

HB