I don’t carry any. The only British photo IDs I have are my passport and my driving license. I might carry the latter, but when I got it there were instructions that the “counterpart”, which is a fairly large sheet of thick paper, must be kept with it at all times. As I do not want to carry the counterpart, I do not carry the license card either. In Britain, if you are stopped by the police when driving you are not legally required to produce your license on the spot, although if you do not have it, you are required to produce it at a police station within a few days.
I do not understand the reasons for the rule about the “Counterpart”, mind you, and if it were not for the explicit instructions to keep them together, I would certainly carry the driving license. But no-one has ever actually asked to see it.
I carry my chip and pin debit card to pay for stuff, and that has my name on it, but no photo.
In the 20 months or so I have been living back in Britain, I have never been asked for, or felt a need for, photo ID, except when I first opened a bank account, when I used my passport.* What I have been asked for, on a couple of occasions, is a utility (gas, electric, or water) bill that has been mailed to me, as proof of address. This was a problem when I first arrived back here from the US because one bank refused to let me open an account, even though I had money to put into it, and photo ID (British passport), but not a utility bill (
:(). (At that point I had only been back in the country a few days, and, in any case, did not yet have my own place and was staying with my cousin. Furthermore, it would probably have been very hard to get a place of my own to live, or, indeed, set up an account with a utility company,without a bank account.) The problem was solved, however, by going to a different bank, across the street, where they were less assholish.
Anyway, although Britain may be regulated more than the USA in some ways, on the whole I think it is fair to say (having lived for 20 years in the USA) that British people have less bureaucratic paperwork (both governmental and private) to deal with than do Americans. This is certainly very much the case with the health care system, but also, I think, income tax and other things too. We do not have to spend so much time filling out forms (or sorting out bureaucratic snafus) as Americans do.
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*Perhaps I also had to show my passport when I first went to a doctor and re-established my standing with the National Health system. I can’t remember for sure now.