Why "The rule of law" is the cornerstone principle of the UK constitution?

For the simple reason that "the rule of law" implies that every citizen is subject to the law, including law makers themselves. Also known as nomocracy (the legal principle that law should govern a nation, as opposed to arbitrary decisions by individual government officials), it is a cornerstone principle because it means that the law, whatever it is applies to all people no matter what their station in life is from the King down to the lowest meanest beggar all are treated equally under the law. Thankfully, this principle is still, despite what some people would have you believe, adhered to in the UK.