Forget the oil, the associated islands to the south gives the UK it's historic rights to its territories in Antarctica - which whilst currently unexploited for environmental reasons, are worth untold trillions in the future.
https://www.bas.ac.uk/about/antarcti...ection/mining/
https://www.princeton.edu/~ota/disk1...926/892606.PDF
https://en.m.wikipedia.org/wiki/Brit...ctic_Territory
https://www.theguardian.com/news/200...ca.sciencenews