It's not entirely clear the Northern Isles are actually British anyway. They were mortgaged to Scotland by Denmark and Norway in 1468 and 1469 as the dowry for Margaret when she married James III, a mortgage that could be redeemed if the cash was later forthcoming.
The curious thing about the mortgage is that it had no time limit on the redemption, something that remained an active bone of contention for hundreds of years afterwards. James VI performed some fancy diplomatic footwork to avoid having to respond to an attempt to pay off the mortgage - it was never quite the right time, alas - and there were subsequent approaches. The last one I know about was King Frederick V in the mid 18th century.
Nobody's ever been able to produce proof that the Danes (who got the islands of the northern sea when they split with Norway) renounced that right, and the Danes certainly don't think they have.
There's still plenty of oil up there... (possibly a billion barrels under Yesnaby near Stromness) and who wouldn't want to have the jewel-like Saxa Vord? (Don't answer that.)