it doesn't matter that england or wales aren't independent countries. the correct way to refer to them is country.
The UK is a dynastic monarchy that calls itself a democracy despite having no checks and balances and not having ever elected its head of government or head of state. It also calls a bunch of oral traditions a "constitution." It doesn't get to tell others what words mean.
the UK itself doesn't even have a written constitution. i guess you're saying that the UK isn't a country then?