I do find it hard to believe this was basically pilot error through disorientation. Surely for these two highly experienced presumably IR pilots, it should not have been a big deal? Ok it was probably pitch black soon after transition, but there is nothing resembling high ground to bump into and weather was presumably clear. But this would surely have been a fairly straightforward Cat A departure with ground references then transition to instruments soon after rotation at TDP and climbing away? It seems the aircraft got considerably further away from the take off point than G-LBAL - which was indeed pilot disorientation in fog at night - which might indicate there is a bit more to this.
I'm not familiar with the 139, but could the understandable rush to get airborne have meant that the instrumentation (especially gyros and AI function etc) was not fully on-line, resulting in unreliable instrument indications so early in flight, with obvious consequences?