Just to add some clarity to the "whose oil" it really is debate
I've uploaded the oil dividing lines made up by the then DTI
oil dividing lines.pdf
also
The Continental Shelf Act 1964 and the Continental Shelf (Jurisdiction) Order 1968 defines the UK North Sea maritime area to the north of latitude 55 degrees north as being under the jurisdiction of Scots lawmeaning that 90% of the UK's oil resources were under Scottish jurisdiction.