The UK has a constitution, just not one that is codified in a single written document with a special privileged status. (In practice, there is also a lot more to the US constitution than what’s written down in the document referred to as ‘The Constitution’.)

"The Annotated Constitution" is that more full version you refer to: https://www.law.cornell.edu/constitution-conan

Kindof a look inside the sausage.