My daughter loved all of these at about the same age:
Gobbolino, the Witch's Cat, The Adventures of the Little Wooden Horse, both by Ursula Moray Williams,
The Dolls' House, Miss Happiness and Miss Flower, both by Rumer Godden,
Poor Cecco, by Margery Williams Bianco
Green Smoke, Dragon in Danger, The Dragon's Quest, all by Rosemary Manning,
the Ramona series, by Beverley Cleary,
the Sophie series, by Dick King-Smith,
the My Naughty Little Sister series, by Dorothy Edwards,
Teddy Robinson, by Joan G Robinson,
Paddington, and Olga da Polga, both by Michael Bond,
the Wombles series, by Elizabeth Beresford,
the Mr Majeika series, by Humphrey Carpenter,
The Animals of Farthing Wood, by Colin Dann,
The Voyage of QV66, by Penelope Lively (amazing book, great adventure story for kids and clever satire for adults),
the Mrs Pepperpot series, by Alf Proysen,
the Worst Witch series, by Jill Murphy,
Wild Robert, Chair Person, Who Got Rid of Angus Flint, all by Diana Wynne Jones,
the Horrid Henry series, by Francesca Simon,
the Mystery (Five Find-Outers and Dog) series, by Enid Blyton,
the Little Grey Rabbit series, by Alison Uttley