An ex colleague of mine had neither passport nor driving licence when she was executor for an old uncle and needed to deal with various banks and building societies. Most of whom insisted on one or the other for photo ID purposes.
However she was a quietly determined person and held her ground in maintaining that since neither was a legal requirement in the U.K., they were not entitled to insist.
Eventually they gave in, though I forget what they accepted instead. A few years later her bus pass would probably have done, but she had yet to reach that stage then.
ID cards for everybody would solve a lot of these problems, though I do realise that criminals cloning them would be an issue now. And I certainly wouldn’t like to be required to carry one at all times, which AFAIK does happen elsewhere in Europe.