There are a few UK based consultancy companies that investigate accidents and incidents on behalf of insurance companies or lawyers (where litigation is involved). Typically, their investigation is at least as thorough as that of the AAIB.
Might be worth googling for them and see if any trainee investigator positions are available.
M9 (Works in the same job but in the Oil/Marine sector though we do get involved in Jet A-1 research

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