Bag of Bones (H Fantasy) - Helen Cresswell
"Griselda Dogberry wishes something exciting would happen to her. Then she finds a bag of bones hidden in the park. In a melting blur these bones develop flesh and fur, whiskers and a tail, and a magical cat steps into her life. Little does she realize that a powerful danger has been unleashed."

I read this a long, long time ago. I have been trying to figure out who it was by and what it was called for some time and now that I have I am so very glad. This was one of those stories that was magical enough to stick with me into my adult years and, even now, I still think about it sometimes.