But what currency would they use? Seems unlikely that the British government would let them issue GBPs without political union. The Euro? Well, I guess that’s a possibility if they don’t mind substituting German overlords for English.
No, they can’t use the British pound if they separate.
Nor would they be admitted into the EU any time soon.
They could actually use the pound without being able to issue them - Zimbabwe switched to the U.S. dollar when their own currency melted down - but it means that their monetary policies would be under British control. I doubt if that would be acceptable in the long term. The Euro is the obvious alternative but Scotland is not a member of the EU separately and Brussels would dictate monetary policy. There was a Scottish pound before the Unification Act and I believe they're still being printed, but they're capitalized by the British pound. The Irish ran a separate system until the Euro, but IIRC they kept large deposits in the Bank of England to back it.
That's about all I know from a purely amateur POV - grateful for correction by anyone with greater knowledge.