Thanks for cheering me, Hildegard. I'll admit to a personal slant on this: my wife has managed to have none of the acceptable documents (she is a stay-at-home Mum receiving no benefits apart from child-benefit, and that won't do as a letter from a benefit agency has to be dated within the last 3 months). Fortunately she has had a passport so it's been a matter of renewing rather than starting from scratch. A surprising number of people, though, really do have no proof of identity whatsoever.
Linda.ff, I appreciate the link to the citizen-card; unfortunately it's not on the bank's list.
sbhoa, I agree completely with your logic. Apparently the government does not. Our bank's argument is that it's not their fault they're having to ask my wife to prove her identity (despite her having been a customer for more than a decade), but this is the result of "new government rules" that oblige them to have photo-ID of all their clients. So, in effect, according to the bank, we are legally obliged to have photo-id(*), despite the state not providing it. You are also quite right: the cost of being a citizen is paying taxes; that cost should buy us our ID card without it being an extra fee.
I have to admit, though, that the citizencard looks like a jolly honest attempt of a bunch of organisations that are obliged to know the age of their clients, to plug a hole in the UK's administration. This quote from the gov.uk website sums it up:
Identity cards were scrapped in 2011 - they’re no longer valid and you can’t use them as proof of identify.
You don’t have to return your identity card. You should destroy it or keep it in a safe place.
The fee you paid won’t be refunded.
The government securely destroyed the personal details of everyone who had an identity card.
("We made you pay/lured you into paying. Then we took away the thing you paid for. We didn't give you a refund and won't. And instead of retaining any idea who our citizens are, we decided to throw away the data").
The UK's foray into identity cards was ill-judged, ill-conceived, ill-executed, and basically a mess. The fee back in 2011 or so was going to be somewhere between £30 and £60 per card, though rumours had it the system was so expensive that the true cost was around £300 per card; Linda.ff's CitizenCard is only £15.
(* edit: or be interacting with the state by post within the last 3 months)