You don't have to show ID to buy alcohol, knives or solvents unless you look underage. Also, I've never been asked to show any sort of id to book into a hotel in the UK.
Last time I claimed JSA (a few years ago now), I don' recall having to produce id either (but I could be misrembering this).
Also, there's big difference I'd suggest in having to own a passport or driving licence (i.e. photo id) and just having proof of residence (e.g. utility bills.)