In UK the AAIB usually advertises vacancies. Assuming your enquiry is for an Ops (ie Pilot) Inspector's position, they normally expect you to have good all-round experience on heavy public transport aircraft and, if they are after a helicopter background, this will likely be somebody with North Sea etc CAT experience.
Being a tp is not a pre-requisite, though a few of the present establishment are so qualified.
Pay used to be an issue: the civil service couldn't keep up with the commercial sector, but I understand that there has been some catching up in the past few years.
If you are genuinely interested and are a potential recruit, you could try asking AAIB for an informal visit.
Cranfield University runs Accident Investigation courses. The AAIB send their personnel on these! You can attend £rivately. There is a Short course and a Long one: depends on depth of your £ocket! Some airline companies will sponsor their Flight Safety staff on these courses. It's also possible to do a course in USA: at least one university there offers short courses.