^The thing is, the title "chancellor," in modern usage, is essentially equivalent to "prime minister." As I suggested before, the chancellor and emperor could've been two different people, like Gowron and Kahless in the TNG era, or like the British Prime Minister and Queen -- one is the head of government, the other is the reigning monarch.
Only problem is that in modern usage in the UK (which is your example) - the Chancellor is not the Prime Minster but your main point that they could represent two different functions stands.