John Blakeley's excellent post brings us back to the core problem here, which is the systemic flaw that has always undermined UK Military Air Accident Investigations; that the operator investigates its own accidents. Even in these days of a supposedly "independent" MAAIB, that still remains the case.
Personally I find the insinuation that civil police input into that process could undermine it as risible. However, the obverse is just as unlikely, for the civil police have long known that illegal orders were made by RAF VSOs to subvert the UK Military Airworthiness Regulations which were suborned at the very highest levels of the High Command, but have shown as much willingness to act on such evidence as the RAF Provost Marshal, ie none.
The story here isn't the supposed primacy of the civil police in Military Air Accidents but the primacy of the High Command in producing the Investigative Findings that it requires. Unless and until UK Military Air Accident Investigation is separate and independent of both the Regulator and the Operator (which in turn must also be separate) then avoidable Military Air Accidents will just go on happening for lack of proper Investigation