Awful accident. My condolences to the families and those at LEA.
That video is troubling me. The length of debris field beyond the initial impact in the trees makes me think that both engines were running and the impact at a very high energy state. There's a lot of speculation on here about OEI or disorientation/loss of control. I don't buy the instrument failure option, it's likely to have had an analogue cockpit and a mix of electric and air powered instruments.
So if disorientated for another reason (wx) height/speed/roll/pitch would, for me involve controlling the speed with a power reduction and a lower energy crash if they didn't recover in time. As it was an experienced Captain/examiner I'm ignoring any possibility of crew error for now.
That's leaving me thinking they knew their orientation, the engines were good but for some reason they couldn't control the aircraft - elevator failure, flight control cables or similar - and an attempt to control pitch with power until out of height and options and by now carrying substantial airspeed.
Stapleford seems a harsh environment (grass and with that asphalt transition) to thrash a King Air in and out of daily - how many hours were on that airframe and what could have critically failed during take off to cause a loss of pitch or perhaps roll control?