Could someone provide a full list of all the class/cabin codes used by
British Airways to indicate which type of ticket a passenger is flying
in.

These numbers seem to take the form A/B, where one part indicates the
cabin (first, economy etc) and the other the type of ticket (free,
fullly flexible etc). But there appear to be many different
combinations for tickets that seem to be identical. Eg. an economy
class short-haul flight can be classed as both M/X, M/N and M/O.

This may be helpful:

http://en.wikipedia.org/wiki/Travel_class

Best regards,
Rainbow