Ultimately the question to be answered is "Why no Rotor RPM?".
One would logically conclude that simple fuel Exhaustion/Starvation itself would not lead to any situation that would, in and of itself, lead to no Rotor RPM. Logically, the two engines would cease running in a sequence several minutes apart.....if the usable fuel was totally consumed.
In a Fuel Starvation situation....it does not logically follow that both engines would be affected unless it was fuel contamination and again....it would seem both engines would not shut down simultaneously.
Even if both Engines failed simultaneously without any warning.....that alone does not explain the loss of NR.
Thus far, physical evidence shows a MGB that appears to rotate normally and at least one engine driveshaft that when rotated by hand drives the MGB. The MGB has overriding clutches....thus even a seized engine cannot stop the MGB.
Flying Bull presents a good suggestion for a situation that could lead to a loss of Nr. A prior Accident Report discussed at least one Accident with a 135 that resulted from such an event.
Nothing said the by the AAIB has suggested Fuel Exhaustion/Starvation might have played a role in this accident. They also have not indicated any evidence the Engine Governor Controls may have played a role. They give no hint at what they think caused the loss of Main Rotor RPM.
In Sim Training....how thoroughly are Governor Malfunctions practiced by Police Unit Pilots?