Oh, okay, get you.

So, in all honesty, I probably wouldn't say that the UK has a constitution -- that is, there is no well-defined set of rules that are treated in any way different than the others.

The UK had a monarchy at one point, where the monarch had very real political power. Then real, codified constraints were placed on the monarch's power, like the Magna Carta. The monarch could not just disregard these.

So in that sense, the UK was a constitutional monarchy, where political power resided in a monarch who was constrained in a very real sense by a constitution.

The problem is that the process of removing political power from the monarch continued, and today the monarch really has no political power at all.

The House of Lords has also been stripped of virtually all political power.

The UK today is basically run by a simple majority in the House of Commons. I have seen this described as an absolute republic (contrast with an absolute monarchy), which I think is a not unreasonable position to take. There is no rule that constrains the House of Commons other than that future Parliaments cannot be bound by the current Parliament. The House of Commons has overwritten Magna Carta text the same way they would any other law. It does not constrain how they may act. Because the monarch has no real remaining power, the old constitutional rules that did constrain the monarch are basically inert.

The British legal take is that they have an uncodified constitution. That is, they do have a set of rules, but they aren't enumerated and the idea is that there is just some things that people would refuse to do because it simply isn't done.

My problem is that I have a very hard time distinguishing between that and any state that doesn't have a constitution. Surely there are also conventions in every country and situations where ultimately, a leader might be disobeyed.

And it's hard to add a constitution within the current legal order to constrain future Parliaments, as the one rule is that they basically cannot do that. I think that you'd probably have to do a constitutional convention and get both Parliamentary and popular support and say that this is somehow "special" and permits binding Parliament.

My impression is that EU membership was going to be a way to basically bootstrap something akin to constitutional restrictions into place in the UK. Basically, the UK could leave the EU if Parliament wanted, so a majority in Parliament would be where sovereignty was vested. However, as long as they never actually exercised that right, in practice, EU treaty restrictions would be followed, and so that provides a practical framework to build on. The ECJ could say "this law of Parliament violates EU treaties". Unless Parliament then said "okay, we're ignoring EU treaties", possibly via Brexit, then there can be long-running constraints on Parliament. But Brexit kinda nuked that.

I remember wondering on /r/ukpolitics whether there might be a constitutional convention as a result of Brexit, since I would think that Brexit would kind of force a reset on all that.

I also noticed some people in the UK writing things along these lines, that post-Brexit, suddenly a lot of constitutional issues become very prominent and that maybe it's time to codify a constitution. Let me google up an example...

https://www.bennettinstitute.cam.ac.uk/wp-content/uploads/2020/12/The_British_Constitution_after_Brexit.pdf

This document uses the term "elective dictatorship", which I suppose is sort of another way of writing "absolute republic".