There are also people within the universities who spend their lives doing basic research into safety, which is generally built upon accident investigation, and also often consult on accident outcomes.
Pretty much all of them will have a first degree in aerospace engineering, a PPL or CPL, and a PhD in some aspect of aviation safety. They invariably work across the community, including with obvious big players such as AAIB or major airliners.
Obvious names if you want to look them up online (Universities are good for that) would be Prof Graham Braithwaite at Cranfield, Dr Mike Bromfield at Coventry, Dr. Guy Gratton at Brunel, Dr. Stewart Houston at Glasgow.
Both are of course very small and elite pools and whether an AAIB inspector or tenured academic in the field, these chaps have taken a lot of years of study and experience to get there - it's not an early career job, nor one many people will ever achieve.