The cams ring are two ramps, opposite each other in the cam ring so the magneto fires one cylinder, then the other. Any variance of the position of these cams will affect the timing, and getting both cylinders to fire at exactly the same time before TDC is a tall order for something made 60 + years ago and worn, neglected, seized, abused etc. The lift on each cam is very small, but magnified by the design of the L shaped moving contact arm. Wear to this and it's pivot also contributes to a timing difference to each cylinder.
As stated, removing the centre bolt on the contact breaker assembly allows the whole unit to pull out for inspection and maintenance. Yes, the cam ring rotates within the magneto end housing, or at least it should, controlled by the advance/retard cable. It's spring loaded to give "slack advance", rotating anti- clockwise against the clockwise rotating contact breaker.
My guess is that the whole ensemble is seized (good news) or bodged...not so good.
If the simple stuff fails, then with care the end housing can be detached from the magneto body, without upsetting the cup and cone bearing setting. BSA Service Sheet 801 gives a basic procedure for the non manual advance type, so worth reading for what goes on inside, internally both auto and manual types are identical, just how they retard the timing for starting is different. Easier to do with the magneto off the bike and this may be the best way to sort it out in any case.
Magneto is described as AC or anti-clockwise...the direction of rotation when viewed from the drive end. Look for AC on the identity plate, along with a date code. The big number is the Lucas Part Number which specifies the original LUCAS factory parts spec for that particular BSA model application.
Swarfy.