Murphy was born on July 5, 1949, in London. She started making her own illustrated storybooks at the age of 6. She attended art school as a teenager. She later worked with children before becoming a full-time children’s author and illustrator.
Murphy’s first book was The Worst Witch (1974). In it, Mildred Hubble attends a school for witches. She tries to be a good witch but always manages to get into mischief. Mildred also appears in later books, including A Bad Spell for the Worst Witch (1982), The Worst Witch Strikes Again (1980), and The Worst Witch Saves the Day (2005).
Murphy created another picture book series about the Large family of elephants.
Murphy also wrote novels for an older audience. Worlds Apart (1988) follows 12-year-old Susan as she looks for her father.
Murphy won the Nestlé Smarties Prize and the Sheffield Children’s Book Prize for The Last Noo-Noo (2011). This book is about a monster who does not want to give up his pacifier.