The film celebrates the relationship between a small girl named Emily (voiced by Emily Osborne), and her kindly but ailing grandfather (voiced by Peter Ustinov), along with a dog. Emily's playful innocence is contrasted with Granpa's increasing frailty. Aware that he will not be around for much longer, he shares his memories of adventures and days gone by.

These memories are vividly brought to life by her grandfather's tales, beginning with a description of Granpa's childhood and youth in the early part of the 20th Century. Other adventures include a chivalrous tale of Saint George and the Dragon imagined on a bedcover, a fishing trip which ends with a journey down the Thames pulled by a blue whale, a trip to the seaside which culminates in a re-enactment of the Battle of Britain and a Noah's Ark-influenced story, where Granpa's house is submerged and the pair have to accommodate exotic animals. The final jungle section, in which monkeys steal Granpa's storybook, is left intentionally incomplete.

As the seasons pass, Granpa grows frailer, and eventually Emily is left alone with an empty chair and the old man's loyal dog. She leaves the house with the dog and climbs a hill. As they travel, a group of children from her grandfather's stories join them.