Air Accidents should be investigated by the AAIB (or national equivalent) and not by the police, unless there is a strong hint of criminal wrongdoings.
Condolences to all involved.
@HS125: your football analogy hits the mark but still I am afraid this might result in further restrictions to airshows and of course it could increase sponsors/partners' involved in keeping old expensive gear aloft reluctance to keep their hands in the antique aircraft operation.
I have seen a Bücker 131 end a loop a few feet below ground level at Hannover Airshow as a kid, hurting no one and (I believe) with the pilot surviving, but it's a sickening sight when you start to feel that a loop is not going to work out.....