Some English people rebelled against William including Hereward the Wake in East Anglia and Eadric the Wild in Shropshire.
The biggest rebellion was in the north of England in 1069. It was led by Edgar the Atheling who, as the only son of Edward the Exiled, had a blood-claim to the throne. He was joined by Danish and Scottish armies.
William defeated the rebellion but he still didn't trust the English people. In the north-east of England, from 1069 to 1070, he ordered villages to be destroyed and people to be killed. Herds of animals and crops were burnt. Most people who survived starved to death; there were even stories of people turning to cannibalism. William did not care if they had rebelled or not.
Not only was the population reduced by 75% but land was salted (poisoned) to prevent people growing crops in the future. This is called the Harrying of the North.
Even by the standards of the time, the Harrying was seen as excessively cruel. A Norman chronicler, Vitalis, writing fifty years later said God would punish William for his brutal slaughter, but William had achieved his main aim. He was in control of the North, and he had prevented a future rebellion. Now William was able to place loyal nobles in charge to look after his lands. William could then set about keeping control of his new conquest.