Yes, the pound is as much Scotland’s as it is England’s, which is to say, not at all. The pound is the currency of the United Kingdom, the laws of which include a currency union created by and subject to that same set of United Kingdom laws.
Monetary policy within the UK is the responsibility of the Bank of England under a series of Acts of the UK Parliament. For example, though the Bank of England has a legal monopoly of the note issue, Scottish commercial banks are allowed to issue notes under licence. Under the 2009 Banking Act, they must hold sufficient reserve assets (Bank of England notes or gold) to maintain the value of their notes in the event of commercial failure. This is because, strictly speaking, Scottish notes are not legal tender but promissory notes.
Just as withdrawal from the EU would leave the UK no longer subject to EU law, withdrawal from the United Kingdom would leave Scotland no longer subject to UK law, which includes the laws governing the currency union and the laws governing the note issue.
An independent Scottish government could choose to issue a currency called pounds, but it could not choose to issue UK pounds since it would no longer be part of the UK. (There is no prospect of Scotland being recognised as the continuing state as opposed to the ten times larger population from which it would have withdrawn, which would continue to be governed by UK law.) The Scottish pound would thereafter become, domestically and internationally, a separate currency from the UK pound. The exchange values of the two currencies could diverge.
Regarding sterling, Scotland would have two options:
- To ask the rUK to continue the currency union, which was what the then Chancellor specifically ruled out in 2014, or
- To use UK sterling (now a foreign currency) within Scotland as Panama currently uses the US dollar. This places monetary policy in the hands of the issuer of the currency, that is to say, the rUK.