My daughter and I went to Edinburgh before continuing to Bath and London this past August (just happened to be during Fringe), and we both love Scotland. I'd been to London really briefly on a prior trip, and absolutely love it, also - but Scotland is something special. I plan to go back and do a Highlands tour, etc. All of this is to say how jealous I am of you for living there.
I'd wondered if there would be border patrol up there - I was guessing not. We'll grab it just to be safe, but this is incredibly helpful.