It has been suggested in this thread that crews are not trained to cope with a total loss of power at low altitude. I would propose that this is not so. Just consider the regular practice, in the simulator, of recovery from windshear or GPWS warning. In both cases, the aircraft is flown in such a way as to trade kinetic energy for potential energy, in a situation where engine power cannot meet the desired flight profile. In other words, trade speed for height. In these situations, kinetic energy is traded for height right back to the stick shaker, at which point attitude is adjusted to fly at intermittent stick shaker speed.
I would suggest that the crew of BA038 did, instinctively, follow exactly what they had been trained to do. Speed was bled back to the shaker speed and then an attitude adjustment was made to keep the aircraft flyable. Energy management.
There seems to be a perception that the stick shaker represents an entry into the stall regime, with loss of lift and control. This is totally wrong. The aircraft remains controllable and flyable at shaker speeds, as there is still a fair margin above the stall speed.