Looking back of course, it is easy enough to say that the end was foreordained. That was not clear on the day of battle; the Normans were thrown back on their initial charge. Their left wing broke and a rout almost occurred when a rumor went out that Duke William had been slain. He re-appeared and rallied his troops. English losses were also heavy. By afternoon, the English still held their lines and the ridge and it appeared that if nothing changed, Duke William would likely be defeated.
And then - from the Bayeux Tapestry, it is recorded nowhere else - an arrow pierced the eye of King Harold.
The Anglo-Saxons broke quickly after this and were routed and ridden down by the advancing Normans. The body of King Harold lay surrounded by his huscarls and his brothers Gyrth and Leofwine.
Ian Walker describes the outcome:
"Thus the battle reached its fatal climax for King Harold, but as we have seen, it had been a very close run thing. The fact that King Harold did not seize the opportunity offered by the collapse of the Norman left wing and the rumor of William's death has puzzled many. However, we should remember the conditions of his army. A basically cautious man like Harold would be unlikely to take unnecessary risks by advancing from a position where all he really needed to do was stand his ground and force William into submission. If he had held the field at the end of the day, William would have been finished, and he almost succeeded in this, falling just before nightfall. That he ultimately failed was largely because of the fortune of war, and the evidence suggests that it was King Harold's fall to a chance arrow which finally broke English resistance and left the field to the Normans. We must remember that what in hindsight was to prove such a decisive defeat for the English, was in fact balanced on a knife's edge throughout the day."
Brooke, Christopher: From Alfred to Henry III 871-1272. Norton Library: USA, 1961.
Hollister, C. Warren: The Making of England 55 B.C. to 1399. D.C. Heath and Company: United States, 1976.
Trevelyan, G.M.: History of England Volume 1: From the Earliest Times to the Reformation. Anchor Books: USA, 1953