My dd turned 3 in Sept and has absolutely devoured every picture book in the house and we've just culled 40 from her collection to be given to a younger family member.
Were looking for some other first chapter books, we've read book 1 of the worst witch this weekend and dd has been happily chatting to me about the escapades of Mildred and maud so I know she's comprehended the story.
My DD started reading some chapter books at 4 - as well as the Worst Witch, she likes My Naughty Little Sister and Horrid Henry. I'm not a huge fan of HH but the advantage of those two is that each chapter is a stand-alone story, as I think when they first encounter chapter books it can be hard for them to hold the whole narrative in their heads. Or at least that's been true for my DD. Oh, also the Winnie the Witch chapter books do a similar thing and are good fun.
Milly Molly Mandy The Magic Faraway Tree The Adventures of the Wishing Chair Esio Trot Mrs Pepperpot stories The Magic Finger Pippi Longstocking Gobbolino the Witch's Cat The Owl Who Was Afraid of the Dark