Extract from the official report:
"In these extreme conditions (engines 1 and 2 producing no thrust), the combination of lateral and thrust asymmetry and the major thrust/drag imbalance, which could not be compensated for by a descent, led to a loss of control. This loss of control was probably accelerated by the structural damage caused by the fire.
In any event, even if all four engines had been operating, the serious damage caused by
the intensity of the fire to the structure of the wing and to some of the flight controls would have led to the rapid loss of the aircraft."
The evidence points to extreme low airspeed combined with two engines not producing thrust that caused the actual loss of control, but the fire would have caused it eventually.
At MTOW Concorde needs an absolute minimum of 206kts to climb away on 3 engines....263kts and gear up to climb away on 2 engines. They managed 211kts after engine 2 was shut down but at that point engine 1 stopped producing thrust and that was that.
The BEA calculated that had they performed a RTO at the time of realising something bad was happening, they would have gone off the end of the runway doing at least 74kts........atakacs was right when he said they were doomed as soon as the fire started.