I've got a glossy AAIB leaflet (dated March 2002) which says they do about 350 reportable acccidents each year.
2% are the so called 'Inspector's Investigations' - the yellow formal reports - which they claim to do in '12 months' (but its not clear if that's a target or an average or what).
23% are Field Investigations which go into the monthly bulletin in '6 months'.
The other 75% are reported on in the monthly bulletin and are based on the air accident investigation form submitted by the pilot in '3 months'. Usually they don't even view the wreckage (hence their embarrassment over the first of the two identical A109 Powers accidents a few years back).
I assume if the debris is at Farnborough they must be doing one of the first two. If its a formal report its not really overdue yet, though I guess they would have made interim recommendations if there was any major hazard.
Perhaps its a pity they don't do an annual report like the Marine AIB that 'contains information about the branch's performance and accident statistics'.