Do you have any first editions or similar? It might be worth checking out the obviously higher value items, selling them, and then just donating the rest to a charity shop.
I always sell mine on Amazon. It is very straightforward. Find the book - see what price people are selling it for. If it is 1p not really worth it, unless a very light paperback as you will get a standard two pounds eighty to cover postage. If it is worth it you click on "sell yours here" and enter details of condition and how much you are selling it for.
I've tried selling on music magpie but they often say there isn't a demand for a lot of books. Another option is a selling page in your area on Facebook?
I don't know if this is right, but my neighbours buy and sell a lot from car boot sales, etc. They say they never sell books, because they can't charge for postage and packing on books, so it's not worth it as they're quite heavy. The wife told me and the husband did separately, but it seems odd?