Yes it is British oil, but the region that allows that claim to the area is Scotland. If historically Scotland wasn't part of the UK the oil would be either International or Scottish it would be very hard for England to lay a claim to it given the geographical location.

Now if the oil was then inherited by Scotland they would need the EU about as much as Norway does. They would also be able to convince HQs for oil companies and their stock listing to transfer from England to Scotland.

What would be the impact to London and thereby England if the highly improbable but not impossible happening went all Scotland's way? Loss of oil fields, banks, oil companies etc? Would England really be better off or would it be at a loss?

You would also have the Royals in England all year round. Surely that is a cost to far.