It's not so much that the regnal numbers reset as that they weren't really used before then.
If we look at the pre-Conquest kings in England, we don't see regnal numbers. If we look at the kings who had names that were repeated, we see:
King Edward the Elder (899AD - 924)
King Edmund (939 - 946)
King Edward the Martyr (975 - 978)
King Edmund Ironside (1016)
King Edward the Confessor (1066)
The Anglo-Saxon and Wessex kings didn't use regnal numbers, only nicknames. It's worth pointing out that the first King Edward had no nickname during his life: the first time he was referred to as "Edward the Elder" was in a historical work written after the time of Edward the Martyr (the 'Vita S. Aethelwoldi', or 'Life of Saint Aethelwold', by Wulfstan). The addition of the nickname "the Elder" was how the earlier Edward was distinguished from the later Edward in this work.
So, there were no regnal numbers to be reset after the Norman Conquest. These were introduced by the Norman kings themselves, starting with King William II, son of King William I. The Normans had been using regnal numbers for the past few generations in Normandy before the conquest of England: Duke William I and II, Duke Richard I and II and III. They simply carried on this tradition when they became kings of England, starting with King William II, the son of King William the Conqueror.
And, when the first king who used a pre-conquest name, Edward (his father named him after Edward the Confessor), came to the throne, he was just King Edward. Full stop. No nickname, no regnal number. He became King Edward I only in retrospect, after his son became King Edward II. Because they were part of the Norman dynasty, not the Anglo-Saxon / House of Wessex dynasty.
Since the Norman Conquest, every new dynastic line on the throne of England has based its claim to the crown on its descent from the previous incumbents. And, one way to maintain that claim is to continue the regnal numbers of the previous monarchs. The Normans didn't do that because they weren't basing their claim on descent from the Anglo-Saxons / House of Wessex.
There were no regnal numbers before 1066, they were introduced by the Normans who had picked up the habit from the French.
At first the numbers were not reset, there were two official titles. James II 's full(er) title was James II of England and VII of Scotland.