Still children's but has he read The Chronicles of Narnia? Also what about Cider with Rosie? Or, not a classic as such, but some of the James Herriot collections are more child friendly or indeed the originals as I can't remember anything awful.
Do you have any good 2nd hand bookshops near you that you could let him loose in?
Agatha Christie - not exactly classics, but good “in betweeny” books between children's and adult’s. Some of the younger terry pratchetts - Maurice or The Wee Free Men? More actual classics i remember liking in your teenhood - Maybe a bit young yet, but Catcher in the Rye and later To Kill a Mockingbird? Daddy Longlegs or I capture the castle? (If he doesn’t mind female protagonists), and similar to Tom’s Midnight Garden is Charlotte Sometimes. if he likes scifi or comedy, The Hitchiker’s Guide?
Northern Lights, The Amber Spyglass etc... Goodnight Mr Tom Swallows and Amazons The Boy in the Striped Pyjamas A Wrinkle in Time The Indian in the Cupboard trilogy The Hobbit My Family and Other Animals Treasure Island The Secret Diary of Adrian Mole Cue For Treason The Adventures of Huckleberry Finn Tom Sawyer The Sword in the Stone The Book Thief Private Peaceful and War Horse Five Children and It Swiss Family Robinson
I've a 11yo. He loved the James heriot books (though they convinced him not to be a vet) He is currently working his way through Malcolm Saville's Marston Baines series. He loved his Lone Pine Series too. 39 Steps Stalky and Co Cue for Treason Swish of the Curtain series Swallow and Amazon series Bannermere Series Various Monica Edwards Box of Delights (and the Midnight Folk) Biggles Alex Rider (not classics but he loved them) Dark is Rising Series Chrestomanci Series Black Beauty
The Little House on the Prairie books are fab and I think boys often miss out on them because of the saccharine TV series but they are full of life and death adventures. Try Farmers Boy first to get him into them.
Otherwise what about all those WW2 books we read as kids like The Machine Gunners, Carrie's War, When Hitler Stole Pink Rabbit etc. Or Susan Copper's The Dark is Rising series.