Duke William of Normandy's victory at the Battle of Hastings on 14 October 1066 A.D. did not inherently mean that that William would be king - kings had fallen in battle and their victors had not replaced them in the past. A member of the royal house of Wessex - Edgar grandson of Edmund Ironsides - remained alive although a minor. The Earls of the North were willing to fight as were the archbishops - but in the absence of a clear leader (militarily or politically) to lead, the coalition began to quickly break up. By late October - within two weeks of the victory - the English leadership had submitted and William was crowned King in December 1066 A.D.
(William The Conqueror's Conquest of England - Source)
William returned to Normandy in 1067 A.D. laden with treasure. He had already begun granting lands in the south to his followers. But a delayed reaction set in: his followers began to usurp land and churches and began building their own residences. The Normans, unlike the Danes and Norwegians, spoke a language completely unlike Anglo-Saxon, and followed different manners. A movement began growing to support Harold's son Godwine, who although young and inexperienced had the power of his father's name. A somewhat disorganized resistance began to grow and burst into flame. It was centered at Exeter, which was laid siege to and overrun by William. Harold's sons Godwine, Edmund, and Magnus fled - to the Hiberno-Norse kingdom where their father had fled in 1051 A.D. Gathering mercenaries, they reinvaded England in the summer of 1068 A.D. with a series of raids along the coast until they were caught in open battle in 1069 A.D. - they escaped, but the bulk of their troops did not.
This ended the active attempts by Harold's family to regain England; his mother and sister fled to Flanders. Some of his sons and one daughter ended up in the court of the Danish King Swein. We hear nothing of the sons after 1075 A.D. but Harold's daughter Gytha was married to Prince Vladimir, a prince of Smolensk in the land of the Rus. He, as well as his son Msistislav became Grand Princes of Kiev. One of Msistslav's daughter's married a Danish noble whose son became the Danish King. The current royal houses of Denmark and England are descended in part from this line; thus in a way King Harold's legacy lives on. Another son Harold fled to Norway and disappears around 1098 A.D.; another daughter Gunnhild became a nun until kidnapped and marrying not one but two earls.
The rebellion which Harold's sons had set off in 1068 A.D. continued to burn into 1070 A.D. especially in the North. William invaded with brutal force and devastation, so depopulating the North that it had to be re-populated in the 12th Century. By 1071 A.D when the end of guerilla warfare ended under such men as Herward the Wake, Anglo-Saxon resistance was essentially done.
Among the upper echelons of Anglo-Saxon society, the dissolution was almost complete. After 1075 A.D. there were no Anglo-Saxon Earls and only a few mid-level authorities such as shire reeves. Most Anglo-Saxon noble families were dispossessed of their properties, by 1086 A.D. only 5% of land south of the river Tees in Northern England was in the hands of Anglo-Saxons. By 1086 A.D. no bishopric was held by an Anglo-Saxon, and only a few abbots remained.
In the 1070's, a fleet of 235 ships left England, carrying warriors and families to the Byzantine Empire and Constantinople. Byzantium is need of warriors and the Anglo-Saxons could fill that need. The Varangian guard, the elite unit originally formed of Vikings and the Rus (Harald Hardrada had served there) came to be heavily replaced by Anglo-Saxons, where the "axe bearing barbarians" and their descendants loyally served the Byzantines Emperors through at least the Fourth Crusade (1204 A.D.).
A final historical note: In 1100 A.D., Henry the 1st, Duke William's grandson, married Matilda (Edith), the daughter of Margaret of Scotland and Malcolm III. Margaret was a daughter of the Athling Edward that had returned to England in 1057 A.D. With this marriage and the children of Henry and Matilda's marriage, the royal house of Wessex in some sense regained the throne of England.
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