How is it not?!
The UK is a Representative Parliamentary Democracy, so it's very much part of the British Constitution. The exact same holds true with a Labour PM in post in the same manner.
We don't and never have elected PMs. What we do is elect a party to government and the governing party selects the PM. Again, the exact same holds true for Labour.
We do consent to the constitutional arrangement each time we vote, for example. And we are taxed on the basis of Parliamentary Representation.
The UK is in the Top 20 in the Democracy Index. You might be surprised which countries we're ahead of - France, Italy, Portugal and Japan are all lower down the ranking than the UK whereas the Republic of Ireland is literally just 0.06 points ahead of us equating to just one place above.