I am pretty sure that Oxfam take books, so I wouldn't give up on the Charity shop front.
What about a car boot sale, or ebay ?
Check with www.abebooks.com to see if any of your books have any value before giving them away, though.
Local groups often have fundraisers when they have book sales (Ladies'sCircle , Women's Guild etc)
Or you could have a look for local second hand bookshops...they wouldn't give you much for them, but at least you would know that they had not been wasted.
Your local doctors' surgery might welcome a few for their waiting room.
Good luck. :-))