If the note is issued by a Scottish or Irish bank, then just walk into any local branch of the bank to exchange them. They cannot refuse to take their printed own notes even if they are no longer in issue. Having said that, I know of no Scottish or Irish bank that have discontinued bank notes in recent history.

If it is the Bank of England, just walk up to front door of the Bank of England, smile at one of the men in the pink tailcoats and top hats at the door and tell them you want to change an old note. I think they do it just inside the front door or they may ask you to go around to the museum entrance by the side of the building (opposite from the Royal Bank of Scotland branch). The museum is a reasonable visit if you have the time.