Lots of those classic books have mature themes that are not appropriate for children of this age so I wouldn't expect a 10 year old to read them.
My dd wouldn't read them as she said they were very boring. So we did what Sudberger7 said, we read a chapter out of each of those books. We talked about the meaning of what we had read and we looked up words. It exposed her to different ways of structuring writing as well.
It also lead to her realising that some of those books are actually quite interesting. She read "A Christmas Carol" herself after we did the first chapter as she really enjoyed it and my 7 year old has also really enjoyed it! She also enjoyed "The Hound of the Baskervilles" which was last year's text. We hadn't actually read that before the 11+ but she came out the exam and asked me to get her the book as she enjoyed the text in the exam!
I wouldn't get too hung up on reading all of them but if you do a chapter of each, you can get a wide exposure to very different styles of writing as well as different vocab.