I've never worked for AAIB, but have worked alongside them on a large number of occasions (and been written about by them once) and I hope that they won't mind me saying a few things about my perception of the working environment. (I hope not anyhow, since I'm quite certain that they know who I am!)
AAIB is a small but quite well resourced organisation based on the edge of Farnborough airfield. They are part of the Department for Transport, and independent of the CAA. Their role is to investigate accidents and to make recommendations which should prevent future accidents.
The majority of AAIB's staff are termed "Inspectors of Air Accidents" - with a loose hierarchy within that headed by the "Chief Inspector of Air Accidents" who reports to a cabinet minister - giving him the necessary clout and authority.
The Inspectors are in two branches: ops (operations = Pilots), and engineering. There seem to be about twice as many Engineers as Pilots although in general most of the Engineers fly at-least at PPL level, and most of the Pilots seem to have a pretty damned good grasp of Engineering.
The Ops Inspectors are generally ex-airlines, and usually maintain currency on some appropriate large type via an airline-AAIB arrangement.
The Engineering Inspectors come from a wide variety of professional backgrounds, although from what I've seen the standard "new boy" is probably CEng + 5-20 years post qualification experience. There is a tendency to prefer, I think, aeronautical engineers with a fair bit of experience with complex aircraft systems - although that could be design/operations/civil/military. I believe that the branch pays for a certain amount of flying for the Engineers, to keep them current.
I've no doubt that the branch's senior management have a continuous strategy on the profile of the branch's engineers and pilots - so, for example, if they currently lack somebody with experience of helicopter systems, or EFIS analysis - then the next recruiting round will give some preference to people with that knowledge. This does mean that, not knowing what thinking is going on at the top, there'll be a degree of luck about any application.
On the other hand, it's clear that there's a profile preferred at AAIB - good breadth of knowledge, excellent interpersonal and reporting skills are almost certainly top of the list.
There are also a few other specialists there - in particular engineers who do ADR analysis, and technicians who look after the in-house facilities.
Another thing I notice is that very rarely have I ever met anybody who *used to* work for AAIB, unless they left at retirement age. It does seem to be a job which people enjoy very much, despite the obviously rather unhappy subject matter. Historically, their job adverts also do offer very competitive salaries - at-least for the Engineers (around the £50-£60k mark as Mark1 said). I've certainly found that AAIB inspectors who I've worked with have always been extremely able and pleasant professionals who I've never failed to learn from and enjoyed working with.
Various of the branch also fairly regularly give public talks, particularly to RAeS branches, on the work of the branch - it might be worth attending one of those.
G