It is completely non-sensical to expect such a nation to have a single document where the constitution is written. It's fucking easy to just write a constitution on a single piece of paper when it's done upon forming the country. It is extremely hard when you have laws going back to the 13th century and you ran a global empire up until the 1950s. It absolutely does have a constitution, and it's a constitutional monarchy, but it simply doesn't have it written on a single piece of paper.
What I'm far more interested in criticising about your idiotic comment is instead that it's just logically flawed. The critique itself originates from Princeton University, which is not a British institution, and the BBC is simply writing an opinion piece on it. Furthermore, what exactly does the BBC have to do with the politics and history of why the UK doesn't have a single piece of paper outlining its constitution? Your comment is practically just an ad-hominem.