I would be able to have a Scottish passport because I'm three-eighths Scottish.
I suppose anyone who would be born in England with at least one parent who is Scottish would also be able to hold a Scottish passport.
It's like the television historian Dan Snow. His British father is BBC television journalist Peter Snow, and his Canadian mother is Ann MacMillan, Managing Editor of CBC London Bureau. So Dan (who is also the great-great-grandson of Britain's WWI PM David Lloyd George) has both a British and a Canadian passport.
Nothing new here BL. I have a British EU passport and a Canadian passport. Anyone born in Britain can get a British passport no matter where else they are a citizen.