Chris, at Hasting, the English army did not run away. Shortly before the Autumn dusk, not long before the battle was bound to end through darkness, the majority of English soldiers charged downhill after the fleeing Norman cavalry. They did not keep to Harold's orders to remain put,
It was a ploy, as the Normans then turned their horses and charged at the English on flat land, the shield wall being by now broken. The Norman infantry then rushed forwards. The English died fighting.
Only King Harold and his Houscarls remained on the hill, and they too fell fighting, as the Norman cavalry attacked, under cover of the archers.
After that, the very last contingent of about 150 English soldiers that remained in formation took up a last stand too, and the French knights, allies of the Normans, charged them.
These last English soldiers also fell fighting, but quite a number of the French knights drowned in the marshes as they charged through that last group.
If the reality had been as you described, the Normans, who won the battle, would have written it in their history pages.
But they did not invent anything, and recounted the facts as they were, and this can also be seen on the Bayeux tapestry.
The same English army had only a few days earlier fought the Norwegians near York, and lost many men in a hard battle.
King Harold is the bravest of all English kings; he and his army stood, fought and died for England!