King Harold butchers/holds for ransom the surviving Norman and Breton troops. If William the Bastard is captured alive, he is doubtless forced to renounce any claims to England and ransomed at a ruinous price. The relations between the Papacy and the English will be soured, with possible a split with Rome if the Pope does not recognize the political triumph of the Godwinsons.
I imagine the following years of Harold's reign will be spent in shoring up defenses in the southeast, and defending against any further Norse incursions. The death of Hardrada will help in the effort of confirming Harold's authority over the North.