AAIB work under them but with full access to everything
That is not the case. The AAIB have full authority with no judicial or police oversight. It is a terribly important factor in getting at the truth and is mandated in ICAO Annex 13.
Unfortunately many other countries do not adhere to this requirement and so the investigation is hampered by individuals not able to speak freely for fear of incriminating themselves.
https://www.app.college.police.uk/ap...jor-incidents/
The AAIB has primacy for the investigation at the scene of an aircraft accident.
The terminology is very much that the police should be helping not leading.
The Regulations make it clear that AAIB Inspectors must perform their statutory duties in cooperation with the authorities responsible for the judicial inquiry. The police may conduct an inquiry to determine if a crime has been committed and/or, if there are fatalities, they may be required to investigate on behalf of the Coroner or Procurator Fiscal pending a formal Inquest or Fatal Accident Inquiry.
Taken from
https://www.gov.uk/government/upload...High_amend.pdf