If Harold Godwinson had emerged victorious at the Battle of Hastings, he would have secured his position as the King of England. The Norman invasion would have been repelled, and the Anglo-Saxon monarchy would have continued. English history and culture would have likely been quite different as a result.
No Norman influence on English society:
The Anglo-Saxon culture would have been more prominent, and there would not have been the extensive infusion of Norman customs, language, and institutions into English society. French influence would have remained limited, and the English language might have developed along different lines.
Different political and social structures:
The political and social structures of England might have evolved differently. The Norman feudal system, which was introduced after the conquest, might not have been established, or it might have taken a different form. The power dynamics between the monarchy, the aristocracy, and the common people could have been different.
Increased Viking influence:
The Vikings had been raiding and settling in England for centuries, and they continued to be a threat even after the Norman conquest. If Harold had won at Hastings, it is possible that the Vikings might have been able to establish a stronger presence in England. This could have led to a more Scandinavian influence on English culture.
Potential Danish rule:
King Sweyn Estrithson of Denmark, who had supported Harold's claim to the throne, might have pressed for a Danish takeover of England if Harold had emerged victorious. This could have led to a period of Danish rule in England, potentially shaping the country's future in ways that are difficult to predict.
Overall, a Harold victory at the Battle of Hastings would have altered the trajectory of English history in significant ways. It is impossible to say with certainty what the exact outcomes would have been, but the Anglo-Saxon culture, political structures, and relations with external powers likely would have been very different.