William recognized this, and made sure that he had a secure place to stay when he visited London. The White Tower (named because it used to be whitewashed) was designed for this. More than that, he built another fortress at Windsor, where he could station troops that would be a day's march from London if he needed support.
William even built two more fortresses within London's walls: Baynard and Montfichet. He couldn't entrust his fortresses to local people, so he put them in the hands of Normans who followed him over the Channel. Baynard and Montfichet were barons into whose hands he put those properties.
Although he might have felt he would be reasonably safe from an uprising, he took to heart the importance of independence to the citizenry of London, the most important city on the island. There still exists his charter, granting to "all the citizens, French and English" the same "laws and customs as they were in King Edward's time."