Yes it does. ALL states have constitutions. The UK constitution is just unwritten.
As usual, at issue here is a problem of definitions.
Let us call Definition A the theory that a consitution is, grosso modo, a series of rules detailing the structure of the state and the relationship between individuals and the state. Probably most modern states have one (although I would not bet on it - Western Sahara anybody? Taliban Afganistan? etc… After all, they might be chaotic, but no one will argue that they are not states). Let us agree that whether these rules are “written” or “unwritten” is another discussion. Let us also agree that whether it is followed or not is also another story. I would like to say, though, that this phenomenon is, in the course of human history, very recent, although it seems to have perdured in Europe under one form or the other since Antiquity.
Let us call Definition B the theory that a constitution is the highest law of the land, the “rules from which all other rules are derived”. I happen to be partisan of this definition, detailed in the “Pure Theory of Law” of Hans Kelsen. It is not that far from a form of “social contract”. This definition is also the one developped by most of the Renaissance and Enlightenment philosphers which inspired the drafting of modern constitutions - of the top of my head I will cite Jean-Jacques Rousseau.
The characteristic of this “highest law of the land” is that it is the one most difficult to modify, as the rules defining its modification are very strict. (eg the U.S.). After all, the first amendment would not be of very great use if it could simply be modified by a 50 percent vote from both house of congresses. Or, to cite Rousseau “plus les délibérations sont importantes et graves, plus l’avis qui l’emporte doit approcher l’unanimité.” (Le contrat social, livre IV chapitre II).
Under definition B, there are many countries which do not have constitutions. But to simplify this discussion let us examine the UK, Israel, and the U.S. All three have Constitutions as understood under definition A. But only the U.S. has a constitution as understood under definition B.
The U.S. and Israel have one document outlining the structure of the state and the relationship between individuals and the state (although in the case of the U.S. at least this document, taken alone, cannot be at all understood, and is effectively worthless, without also taking into account the mountains of decisions of the Supreme Court on the topics of relevance).
England does not have such a document, although it has a collection of rules (most of them, actually, written) outlining how the state is to be governed, and what the relationship is between the state and individuals. These rules were developed (and for the most part, written) over the last millenia, but for the most part are creations of the 19th century.
If one wants to change the U.S. constitution, it is, to put it mildly, very hard. That is why, excluding the bill of rights, it was only modified 17 times in around 215 years (how static - probably the least modified “constitution” in the world). Article 5 explains the process.
However, should the U.K. or Israel want to change one of its very important rules, “constitutional rules” if you wish, they would need… a 50% vote in the house of commons, or a 50% vote in the Knesset. The rules detailed in the Isralie or UK “constitution” (Definition A) are therefore like any other law. Therefore, the Labour Party could, entirely legally, declare, for example, Tony Blair Prime Minister for life. And there is absolutely nothing anybody could do about it. Whatever rules not permitting him from doing so, may be abolished with a 50% vote from the house of commons.
As an example (of the top of my head):
-Tony Blair is modifiying the composition and powers of the house of lords. Such a process would be considered a “constitutional modification” (definition A) in any other country. But Blair can do what he wants. As a parallel, it would be like the U.S. House of Representatives modifying the composition and powers of the U.S. Senate following a 50% vote in the said House.
So no, I really do not consider the UK to have a constitution.
jc