If an aircraft accident involves a fatality then the coroner has jurisdiction, if the accident doesn't then "technically" the police do.
The Police, normally, hand it over to the respective investigative authority ASAP; if Civil then the AAIB, military, then either the RAF/NAVY/ARMY investigation team.
All accident reports in the UK, civilian and military are given to the Secretary of State in there first publishing.
The military will undoubtedly form a board of inquiry, which unlike an accident investigation team, civil or otherwise can attribute blame.