No, 'Brad or I' is definitely incorrect in this context. It's grammatically wrong in UK English or any other version of English. It sounds more 'formal' because 'and I' is correct where many people would wrongly say 'and me'. This is exactly why people get it wrong, because it sounds more formal. "It's Brad or me" is correct because you would never say "It's I". That's the simple rule. Sounding