Not in my, admittedly limited, experience. I've stayed in hotels in at least a dozen countries and under half of them wanted my passport. In the UK it's usually enough to just say my name to the receptionist, they confirm how long I'm staying, ask me to sign a form and tell them my car registration number and then they hand me the key. Quite often there isn't even a form to sign, just a terminal to enter my car registration number to avoid parking fees.

I was asked for my passport in a Premier Inn this summer because they thought I was a foreigner but when I pointed out that I was a UK citizen they dropped the requirement.

In Europe it was mostly Italy and Poland that wanted to see my passport.