Well it does, in written bits in various places, and some as precedent.
However it is a bit more complex. England has a constitution (that collection above), Scotland has a different (and somewhat incompatible) constitution.
The incompatibility being where the seat of Sovereignty lies. In Scotland with the people, in England with the Monarch (but wrested away by Parliament).
So when the two countries formed the new state of Great Britain, and dissolved their prior states, they granted it a minimal constitution. However they couldn't grant more than they had, and the Scottish grantors did not hold sovereignty. Hence claiming that UK Parliament is sovereign is to presume that England annexed Scotland.
That continuing incompatibility is (IMO) why we've never had a single written GB/UK constitution, and probably never will. It will require addressing the fact that we're acting as if Scotland was annexed, and to put that in writing will cause its own problems.
Frankly, the US system isn't exactly a resounding vindication of written constitutions either. Arguably the UK system has displayed considerably greater flexibility. For example the US president is still basically an elected George III.
However it is a bit more complex. England has a constitution (that collection above), Scotland has a different (and somewhat incompatible) constitution.
The incompatibility being where the seat of Sovereignty lies. In Scotland with the people, in England with the Monarch (but wrested away by Parliament).
So when the two countries formed the new state of Great Britain, and dissolved their prior states, they granted it a minimal constitution. However they couldn't grant more than they had, and the Scottish grantors did not hold sovereignty. Hence claiming that UK Parliament is sovereign is to presume that England annexed Scotland.
That continuing incompatibility is (IMO) why we've never had a single written GB/UK constitution, and probably never will. It will require addressing the fact that we're acting as if Scotland was annexed, and to put that in writing will cause its own problems.