The world does not have a single example of a perfect democracy - there are no true democracies. Rather it has flawed democracies. The UK system has its own specific flaws and its own specific strengths. It works so it is a functioning democracy.
I don't recall mentioning perfection, but I don't disagree with you that currently no perfect democracy exists. The definition of functional then becomes a measure of how imperfect a system is, the British system is so imperfect that it dramatically falls short of being functional.