I wrote "norman invasion" instead of "Battle of Hastings" because with this PoD the battle can be fought on another location, because even if Hardold did won at Hasting, he hardly would have won a decisive victory.
With this scenario, Harold crushes the norman army (it doesn't need to be on a single battle) and capture William alive. What does happen under that circunstances? Bonus points if you describe what most likely happens on the following centuries, since England remains predominantly anglo saxon.