I don't really remember being read to - my sister read me Heidi when I was 3 and by half-way through I was reading it myself.
I remember my younger sister had a poetry book my mum would read from. The Jumblies, and The Raggle-Taggle Gypsies, and possibly Up the Airy Mountain, and things like that.
Either my brother or my little cousin had a book called the Churkendoose (they found an egg and all took turns incubating it).
We did have a set of cassettes of the Winnie-the-Pooh stories, which we all enjoyed when I was about 15. No idea who was reading them - google throws up both Alan Bennett and Lionel Jeffries at approximately the right time, but neither shows the image I remember.