"and the Landmark Good Childhood report found that poorer children often had fewer than 5 books in the house and didn't visit libraries."
The barriers to wider uses of literacy aren't only, or even primarily, financial, though. If they were, library use would be higher amongst the disadvantaged, which it manifestly isn't. It's trite to suggest that even in the absence of libraries, you can buy a couple of books in Oxfam for the price of a packet of cigarettes. But given smoking is often held up as one of the reasons why health outcomes are poor amongst the disadvantaged, it's not entirely trite. Oxfam know their own market, and that I was able to pick up three different translations of Sophocles' Theban Plays in my local one a few months ago says they aren't targeting those in desperate need of cheap books.
It's not uncommon to see discussions about issues like this break down into an assumption that disadvantage means benefits and everyone else spends their time reading German plays in the original, but it's obviously not true, and there are vast swathes of the population who don't own many books and yet pay for Sky TV. That's not about material disadvantage, it may not even be about educational disadvantage, it may genuinely be that they'd rather watch football on the telly than read an Anthony Powell novel. Which is a choice. It may be a choice many find odd, foolish and/or incomprehensible, but merely making books available more cheaply isn't going to change it.
In the end you run out of other people's money, and it seems dubious to raise council tax, levied on all, in order to fund making books available to people who wouldn't choose to spend their own money on them. Because unlike opera, parks, roads and hospitals, books have reached a situation where individuals of modest means can row their own boat, and replacing the entire local lending library system with £lots per year of book tokens for everyone in receipt of means-tested benefits might be better all around.
I love libraries, and have been known to visit them when in other cities on holiday, but I'm very suspicious about the arguments around libraries as eternal necessities. We live in an era when books are fantastically more available than they were even a generation ago: the rise of Amazon (et al) and the end of the net book agreement mean that you can buy both minority books easily and popular books cheaply.
Big libraries, reference libraries, may still have a role, and university libraries certainly do. But I can't imagine the things I used a reference library for doing my O Levels thirty years ago wouldn't be better done on-line these days, and for undergraduates and postgraduates journals are now available online, even historic ones. My supervisor says that he hasn't ventured from the department to the library in ten years, and I certainly felt when I used the university library last year whilst doing an OU Arts course that I was paying my last respects to a dying process (and I used it more as a quiet place to work on a Saturday morning that anything else).