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.
(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.)