The UK has a complicated relationship with IDs anyway, they don't have a national ID, no one's mandated to have a passport, and a driving license is also optional (only if you want to drive). The US is almost like that except that not having a driving license is an oddity there.
Indeed - but even if you have a license, there is no expectations to carry it when you drive. If the police request they can give you a 'Producer' which historically was where you had to attend a police station with your license and insurance documents - but they can check insurance online via ANPR (automatic number plate recognition) before they've even stopped you.
Getting into clubs as a teenager was comical - as there is no standard ID most people had 'work ID' that was just a laminated bit of paper. Or would carry a paper drivers license with no photo on it.