David Carpenter's The Struggle for Mastery looks at how the Norman kings and nobility treated the English in the third chapter. First and foremost, they viewed the English as a conquered people in both land and blood. Before the loss of Normandy at 1204, some Norman barons held estates on both sides of the channel. While the lower gentry intermarried, the nobility valued their purity of blood as a facet of their "Normanitas."

King John (1199-1216) was the first Norman king to drop the tradition of formally addressing "French and English" in his documents. As time went on, the Normans became so divorced from their homeland that they were, for all intents and purposes, English. Eradicating the distinction increased loyalty among their English subjects and proved useful for galvanizing them for war against the French.

To answer the question, the kings of England following the conquest were Norman. Until the loss of Normandy, they were buried there as a way of preserving their "Normanitas" and legitimizing themselves as the heirs to William.