I'd say the European assumption would be that there are one or two valid ID cards (a passport and a national identity card), and owning either one would be mandatory. Doesn't then disenfranchise anyone.
It's not mandatory in all European countries though. But I think it's usually mandatory that you are able to identify yourself somehow.
The main way you might be required to identify yourself in the UK is if a Police Officer says either you are suspected of a specific crime, or you are a witness to such a crime. In both cases officers are entitled to you truthfully revealing your name and address as part of investigating the crime, but they aren't entitled to see a photo ID as you may not even own such ID. If you refuse to identify yourself in either of these cases, or the officer believes your answer was deceitful, they can arrest you (which if you were a suspect was likely going to happen anyway).