My guess is that AAIB need at least one of: date, aircraft type or accurate location. The OP does not appear to have any hard data, so he needs the death date from the certificate.
There will almost certainly be local (or national) newspaper reports of the crash and perhaps the coroner's hearing, which you can get to once you have date and location. Main libraries normally have micro-fiched copies of their local papers, catalogued by date.