This is a charming book that reminded me a lot of E. Nesbit and Edward Eager. It was first published in 1955 and has been reprinted in a nice hardback edition with the original illustrations. I'd never read it before, but I would have just loved it as a kid.
Ten-year-old Rosemary plans to buy a broom so she can clean neighbors' houses over her summer break, intending to surprise her widowed mother with the money. But the broom she buys turns out to be a witch's, and along with it she acquires the witch's cat, Carbonel. But Carbonel is no ordinary cat. He's a prince who was catnapped from his cradle as a kitten. He needs Rosemary's help to return to his people.
The story is lively, inventive, and a complete delight. I read it in a few hours and enjoyed every word. Its portrayal of both children and cats is realistic and very funny, and I especially liked that everyone ends up better for their experience, even the witch. I think there are sequels, too.