I think my DM may have read the Beatrix Potter stories and Winnie the Pooh, maybe Wind in the Willows, Jungle Book and Baba the Elephant as I still have the old editions of all those, but I don't really remember her reading to me very much. I do also recall Chicken Licken (and the sky falling in), which seemed to go out of fashion for years before I discovered it again as an older adult - nobody I knew seemed to have heard of it.
I leaned to read quite young (being stuck at home due to long-term illness) and I read Famous Five, Secret Seven and all the other books I could find by Enid Blyton. I also read Mrs Pepperpot (I had forgotten that until a pp mentioned it). We had to learn the Song of Hiawatha at senior school so that takes me back!
We belonged to the local library and I completely exhausted the children's section long before reaching the age of being allowed an adult ticket (age 11 to tie in with the change in schools) so they made special allowances so my DM could take me in to choose suitable books and have extra tickets.