It is my understanding that the acronyms MI-5 (now the Security Service) and MI-6 (now the SIS) stood for British Military Intelligence - Sections 5&6. That implies that there were/are Sections 1 through 4. Are/were there, and what did they do?
Sua
At least some of them existed. Other than MI5 and MI6, I’m not sure if any of them still exist. According to the Encyclopedia of Espionage by Norman Polmar and Thomas B. Allen, they were:
MI1 Directorate of Military Intelligence
MI1(b) Cryptanalysis Section
MI1© Foreign Section
MI3 European Country Section
MI3(b) German sub-section (became MI14 in 1940)
MI5 Security Service
MI6 Security Intelligence Service
MI8 Radio Security Service
MI9 Escape and Evasion Service
MI14 German Section
MI19 Combined Serviced Detailed Interrogation Centre
MI(L) War Office Liaison with Allied Intelligence Services.
There are still some gaps here. 2, 4, 7, 10-13, and 15-18. I guess if they told you, they’d have to kill you.
From Guardian Unlimited - Notes & Queries we have:
I note there are differing descriptions for some of the agencies, e.g. MI3 and MI9.
I suspect disinformation. 
Sua
MI3 looks a lot like MiB. Coincidence?..