Wanting to see the world and unable to live with his uncle anymore, Bunyip Bluegum the koala sets out on his travels, taking only a walking stick. At about lunchtime, feeling more than slightly peckish, he meets Bill Barnacle the sailor and Sam Sawnoff the penguin who are eating a pudding. The pudding is a magic one which, no matter how much one eats it, always reforms into a whole pudding again. The pudding is called Albert, has thin arms and legs and is a bad-tempered, ill-mannered so-and-so into the bargain. His only pleasure is being eaten and on his insistence, Bill and Sam invite Bunyip to join them for lunch. They then set off on the road together, Bill explaining to Bunyip how he and Sam were once shipwrecked with a ship's cook on an iceberg where the cook created the pudding which they now own...