I notice you are using the phrase "constitutional law" now, where as the original question was whether the UK can be said to have "a constitution."

The oddities of this "duck" go far beyond its lack of entrenchment. It also lacks form and definition in the way that a puff of smoke lacks form and definition. It includes such nebulous elements as common law, unwritten convention, and even legal commentary of various law scholars. It's also said to be in constant flux as it evolves over time.

It may be a useful abstraction within the context of UK law to refer to this amorphous blob as the "constitution," but for anyone unfamiliar with the UK's system of government, to say the UK has a constitution is grossly misleading in as much as all of the conclusions the listener will draw from that assertion will be false. It's like characterizing a chicken eating grain out of your hand as being "attacked by a dinosaur." The chicken may belong to the clade "Dinosauria" and may have inadvertently pecked your palm in its feeding frenzy, but in as much as it communicates information contrary to fact, it is a confabulation. At best, it's a lawyer's lie, to coin a phrase.