Quoting FireLight:
The problem with any credible theory is that it has to fit those pesky facts.
And for facts you need the data and evidence to prove a theory.
If evidence remains unavailable, the next best thing is try and simulate the conditions and observe systems behavior against the data available. If the cause is still unknown at this time, apparently something happened which cannot be retrieved from the recorded data.
That brings me to bsieker's clear summary. Focussing on the fuel flow and referring to my posts #590
"Code One . . ." on page 30 and #810
"What if . . ." on page 41 of this thread:
If the investigation remains inconclusive, would the AAIB wage a temporary repair of the aircraft, sufficient to install engines and landing gear/flaps and simulate at least the last minutes of the flight with fully operational systems? Perhaps from the moment the aircraft entered the Lamborne hold.
The engines would only have to operate near approach idle, with the aircraft ground/flight sensing system simulating the in-flight mode. The gear installed to support the aircraft only. Gear retract actuators disconnected from the gear but fully functional with weights attached to simulate the gear extension (the same for uplocks and door actuators). Then perform (including all system selections i.a.w. the SOP) the complete final approach sequence of lowering flaps, gear and consequent engine response to the changing aircraft geometry, changing to the landing configuration. If it was a problem in the aircraft's systems which ultimately exposed itself in the fuel system, perhaps it started during this sequence. Somehow affecting fuel flow, but going unnoticed by the crew until the engines required increased fuel flow (apparently to above approach idle) at approx. 720 ft.
Green-dot