From Written Style Guide
List only the four highest academic awards, unless they cover more than four different discipline areas. The sequence should be from the lowest to highest, with only the highest appearing in any one discipline.
All qualifications should be followed in brackets by the abbreviation of the awarding institution. If more than one qualification is received from the same institution, only the final qualification should be followed by the awarding institution.
Try these sources for abbreviations:
British degree abbreviations - Wikipedia, the free encyclopedia