Similar to ClareK's suggestion, I donate a lot of mine to a local charity that operates an annual book fair.
Doing a Google search of "charity books UK" lead me, not surprisingly in retrospect, to the site of an organization called
Charity Books. They might be just what you're looking for if they are legit.
I know this doesn't help you much, but there's a chain of bookstores (Half Price Books) in my area (Texas) that specializes in buying and reselling used books - hardcover AND paperback. If you can find something similar nearby, they usually offer some minimum recompense for any book in fair condition.