This answer is more political that purely historical; it should have been a comment but I needed the extra space.
I believe you are thinking in modern terms: the state-nation, where the people is sovereign and can elect its own form of government. This concept, stablished as it seems, is relatively new (Age of Enlightment, American Declaration of Independence and French Revolution). Before that, the people sheldom was a political subject1 and was considered under the control of a higher, usually military caste. The idea that english people should revolt because they liked Harold better than Edward was like political-fiction at the time (and it is worth noting that it isn't that such people were never asked if they liked Harold in the first place).
Even the Roman Empire worked this way, with a tiny nucleus of citizens dominating a mass of non-citizens. In the conquered territories, if the chieftain was amenable to submit and pay taxes they would not interfere with him or they would even support him in dominating his subjects; if the local power caused trouble then they would send in the legions.
Later this Roman citizen/non-citizen relationship was changed to a military/civil relationship, with the emperors being so due to its control of the Army. They still used the civilian structures (v.g. Senate) but whenever it became unruly the army would step in to "restore order"
When the Germanic tribes took over they did pretty much the same, they simply destroyed / took over the Roman military and replaced it with its own; what was left was already used to obey whoever was in charge. Those power structures left by the Romans (vg. Church, or local chieftains) simply had to negotiate with the new lords which would be the balance of power; some people could not like it and rebel, but those were not "popular" uprisings but rebellions by local leaders2.
The conquest of England was more or less the same: take out the top dog, destroy organized opposition and then rule; the main difficulty being that you have to reward your allies with lands so you would need to disposses the previous local nobles (at the risk of the occasional local rebellion).
1: There were rebellions in the Middle Ages or before, but mostly due to lack of food and they sheldom tried to replace the stablished order but to lower taxes and similar situations.
2: The most notorious exception would be the case of religious wars, when the invader was of a different religion. For example, many Germanic tribes found it expedient to convert from Arrianism to Catholicism in order to avoid alienating too much their subjects.