Sure they do. The constitution doesen't have to be a single document.
Which is not necessarily a bad thing. The American constitution has basically become immutable at this point while meaningful reform is still possible in Britain.
The US changes its constitution by just having the Supreme Court make things up. As you can see from the Lochner era, this has rarely worked well.
Here’s another page that could probably use the fruits of your research:
https://en.m.wikipedia.org/wiki/Constitution_of_the_United_K...
https://en.wikipedia.org/wiki/Constitution_of_the_People's_R...
Not to claim it's the same situation, but there's a difference between things that are officially true and things you should actually respect. You shouldn't respect most of the US judicial system either.
Could you relate that back to your initial claim that "the UK still has an absolute monarchy", which appears to be both officially untrue and untrue in practice?
https://en.wikipedia.org/wiki/Royal_prerogative_in_the_Unite...
Especially
https://ukconstitutionallaw.org/2013/01/26/tom-adams-royal-c... + https://www.theguardian.com/uk-news/2021/feb/08/royals-vette...
They don't even make the monarch get a driver's licence or pay taxes.
Maybe they could try writing some of that down in a constitution.
If you've ever eaten Indian curry (of the tikka masala variety in particular), chances are, its recipe was British in origin.
While traditional British food might not appear particularly appealing to the discerning palate, Great Britain is home to many a culinary innovation.
To have a constitutional government, you should first have a constitution.