One of the cool things about living in the UK is that there is no requirement that you be able to prove who you are. You don't have to carry an internal passport, an ID card, your driving licence etc.
(This will probably change at some point. One person's Fundamental Human Right is another's Technical Legal Loophole.)
Here in California, you're required to carry your driving licence with you when driving. You're also supposed to have proof of insurance and proof of ownership of the car. Or something like that: I keep a photocopy of something in the car, the registration document I think.
I also have a notion that you're supposed to carry identification at all times in the USA even when you're just walking. I don't know how true this is in theory, but of course it hardly matters at all in practice.
I also suspect that as a foreigner, I should probably have my passport with me at all times. F*** that - losing it would be far too big a hassle. Anyway, I don't look Hispanic, nor do I live in Arizona. (I'll rant about the outrageousness of that some other time, once I can write about it without wanting to smash things.)