They shut down the no. 2 engine only. The no. 1 lost thrust due to multiple surges, due most likely to ingestion of hot gases and/or tyre debris, and/or pieces of aircraft structure. Even if no. 2 had not been shut down, it is not unreasonable to surmise that it would have continued to suffer similar surging and loss of thrust to the no. 1.
Once again, and quoting directly from the BEA report:
"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."