The Enid Blyton Secret Series

Peggy and her younger twin siblings, Mike and Nora, are living with a harsh aunt and uncle after their parents are thought to have been killed in a plane crash. In this first adventure, aided by Jack (a local orphan boy), they run away to live on a deserted island on a nearby lake. They build a house made with the branches of a willow tree, and bring a cow and some chickens across, to provide milk and eggs. They adapt well to life on the island. However, some day-trippers visit and nearly discover them. The local police are also still looking for them and Jack is almost caught when he goes ashore to sell produce at a local market.