We are all british and from the UK, at least for the present, if independence comes to fruition, then there would be a dissolution of these United Kingdoms!
If you know the British person's nationality, ie English or Scots, or Welsh or Northern Irish, then we appreciate it if we are called by our real nationality. However, what we from the Celtic fringes of our nation dislike is when 'English' is used as a synonym for British. I certainly don't mind being called British, because that's what I am, but as I've said... Just don't call me a Brit!
ETA. When I say I don't mind being called British, I am speaking only for myself, many of my fellow Scots And Welsh and Norn Irish DO MIND!)