I ended up sending an email to the UK meteorological office and one of their resident experts replied with the following answer:
" The cloud classification in use around the world today has its basis in a classification scheme developed by a chap called Luke Howard in 1803. Howard was fascinated by weather and kept a comprehensive weather diary for the London area through the first half of the 19th century. When he started making weather observations he soon noticed commonalities in cloud shapes and, presumably both to facilitate making his observations and in keeping with scientific fashions at the time, came up with a cloud classification scheme. As with other branches of science at the time, for example biology, this scheme was in Latin. Howard's scheme classified clouds according to four basic types: Cirrus (meaning hair-like), Stratus (meaning layer), Cumulus (meaning pile) and Nimbus (meaning rain producing) and in time was expanded by other to cover other details such as cloud altitude and compounds of these clouds, for example stratocumulus. As national meteorological services, such as the Met Office, began to form during the late 19th century it was recognised that some internationally agreed standards to describe clouds would be desirable and Howard's scheme, albeit modified, was at the heart of these standards.
A 'cloud atlas' stemming from an international meteorological conference held in Munich in 1891 appears to be the first 'standard' cloud atlas (
International Cloud Atlas - Wikipedia, the free encyclopedia ). This work was then modified before the First World War and then, partly due to the advent of aviation, the International Commission for the Study of Clouds was set up in 1921 and produced an improved cloud atlas published in the early 1930s. After the Second World War the World Meteorological Organization re-visited the cloud atlas and in 1956 formalized it into a publication called 'International Cloud Atlas' which is the basis of the cloud classification scheme meteorologists the world over use today.
So, why Cb and not Cn? This is quite intriguing. A book cited by the International Cloud Atlas, (Clayden's Cloud Studies) which was published in 1905 lists Cu. N. as the abbreviation for a cumulonimbus cloud and implies this abbreviation may have come from the cloud atlas published as a result of the Munich Conference. Ahead of the Munich Conference Cum. Nim. is one suggested abbreviation. The International Commission for the Study of Clouds' work, published in the early 1930s, then lists Cunb as the abbreviation for a cumulonimbus cloud. The WMO's International Cloud Atlas then lists Cb as the abbreviation for cumulonimbus clouds.
The meteorologist who answered your question suspects that the abbreviation for cumulonimbus changed from Cu. N. to Cunb for reasons of clarity and unambiguity and then was abbreviated to Cb for reasons of brevity. These decisions to change away from Cu. N. appear likely to have come about through committee meetings rather than the work of one individual."