Also, were there MI7, MI8, and so on? If they existed, what were their responsibilities?
During the First World War, MI1 (or Military Intelligence; Section 1) was the code breaking department of the British intelligence service, while MI2 which focused on geographical regions, with sub sections handling different accounts. MI2a for example information of the Americas, while 2b handled the Near East and North Africa. This section following the first world war was changed to focus on Russia and Scandinavia before being incorporated into the newly formed MI3. MI4, was utilised during the Second World War as a means to use planes as reconnaissance in that it took photographs of battlefields giving it the name (the) "Photographic Development Unit". This eventually evolved into the RAF's DIFC unit.
The higher up MI's go up to MI19 with various forms and functions some no longer existing. MI7 being press and propaganda, MI8 being communications, MI9 dealing with British POWs and so on.
Some interesting reads are "The History of The Ministry of Defence" As well as; ["Intelligence and security Services"] (http://www.nationalarchives.gov.uk/help-with-your-research/research-guides/intelligence-security-service-records/#9-the-security-service-mi5-and-the-secret-intelligence-service-mi6-records)