That's not true in the UK, there's no ID card here. IMO it's quite a nuisance, for example you need to always bring 2 documents to verify your identity and address for a variety of situations (opening a bank account, even opening a new savings account at the SAME bank, renting a new place, new job, mortgage, requesting information from the government).

Don't get me started on the UK and the ID card. It's stupidity at the highest level. There is a de-facto "ID", your national insurance number (like a social security number). Except it has no ID features, and cannot be changed. So much, much worse than an ID card. As far as practical ID for bars/clubs, people usually just use a driving license, or are forced to use a passport. Complete idiocy.

(However to get back onto topic, most people in the UK will have a passport, otherwise they should have a NINo allocated at birth. For the people who have neither, the GDPR is the least of their worries.)

Fun fact, in Lithuania people are allocated personal number (similar to NINo?) on birth. ID and/or passport is mandatory regardless.

However, personal number is not guaranteed to be unique because of how it's issued. We have funny stories once in a while when people with similar (or even identical) names happen to have same personal number. A photocopy of ID in important governmental or banking actions.

... and a surprising number of official documents have errors in them, minor address or name misspellings, that make them invalid for this purpose.