Let us rephrase the question; What evidence is there we are a democracy? Do the elected listen and act in accord with the electorate? Do your local council do what you want? Does your MP or local councillor respond to the majority will? My experience is no. For instance a majority voted to leave. In a democratic system that would have been the end of the matter. However it is not is it.
To look at your question, puppet state a meme that does not really capture the state of things. Does the state act independently of the judiciary? Does the judiciary act independently from the state? Have we ceded powers to a foreign entity? I think no, no and yes. We now have an unelected bureaucracy dictating laws and the make up of our country without reference to the sovereign people. We the electorate says what does go on and what does not. But apparently not. Our government is on its' knees to a foreign power begging to be let out of class and like a worm on a hook. Why do not the government just say ta-da pal and get about the business we elected them for which is to leave?