I don't think that the original terms are wrong. The Special Investigation Branch (SIB) of the RAFP or RMP is the military version of the civilian police's Criminal Investigation Department (CID). I don't believe that it would have been mistaken for Special Branch, which was/is a totally seperate arm of civilian British law enforcement and had a remit to tackle foreign counter Int issues. It is not beyond the realms of possibility that a military copper was attached to a civilian law enforcement agency and was awarded the MBE for his efforts.
Perhaps Forum member and RAFP specialist Stephen R. Davies may wish to comment?
In fond memory of Corporal James Oakland AGC (RMP), killed in action in Afghanistan on 22 October 2009. Exemplo Ducemus.