The UK does not have a written constitution.The constitution of the United Kingdom is the sum of laws and principles that make up the body politic of the UK. It concerns both the relationship between the individual and the state, and the functioning of the legislature, the executive and judiciary. where as US constitution was written by British colonial rebel leaders on libertarian principles and values consistent with English libertarian thinking at the time and since.
The UK is still theoretically an absolute monarchy, and it's only custom and convention and a few laws that stops it being one. Most notably, the Bill of Rights 1689 prevents any law being made without the consent of Parliament. That's the key one that stops Queen Elizabeth II doing just as she likes (and it was a response to Charles I, and his son King James II who failed to learn from his father's mistakes). Look at it logically and it's all amazingly haphazard, but everyone in a position of power knows what the "unwritten rules" are and so far it's worked. It's all wide open to a potential Hitler taking advantage of all the legal gaps, but while there isn't one, nothing will change