What do you mean by “classic books”? Do you mean books by famous authors——like Dickens, Austen, Hemingway, Trollope? If so, the UK is stocked to the max with hospice shops that carry these. You can also go to ebay.co.uk and search “classic book set” and find something there, too. There are used book shops all over England and if you want to really find some good used bookshops go to London…or better yet, hit the Oxfam Bookshop at Oxford filled with good used bookshops and while there, go to Blackwell’s. Go to boot sales, too.
You can find books everywhere in England…and classic books, too.
I am a bibliophile and my problem in England is not in finding good books…it’s in figuring out where to put them all!
Best of luck.