I've heard of that scheme, but can't for the life of me remember what it's called, not what you've said Bean, something else, tho I know the site Ken use to post on..might be worth playing around with words on Google, Georgie? There again, seems as though you've got too many, usually it's for the 1-2 books you read when journeying & want to offload, I think.
Our Charity shops will collect, btw, have you asked? And I think it is worth offering boxes of books on Freecycle, sure they'll go..peeps wot do carboots will be happy to make cash for themselves out of them, if you're happy for that. Boxes from the supermarkets, they always will hold back some stout ones for you if you ask.
All I can think of atm, Lish
It's some years ago now & I don't know if it would still happen, but I offloaded absolutely loads of ours at a local hospital - I was visiting every day so I could take them each time I went.