We'd probably use the pound in the interim. I'd campaign for us to adopt the rouble. That would really annoy Mrs May.If the outcome of a second local referendum was independence, you wouldn't need a second Brexit referendum. You'd no doubt be remaining in the EU with the EU accepting that after a bit of hassle about the currency you'd use. The euro, the pound or a new one of your own.
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As to the EU. There were people up here campaigning for independence last time based on the fact that they wanted out of the EU and David Cameron had said that's what would happen if we left the UK.
As my old granny used to say, "there's nowt as queer as folk."