Joe, a young boy living in a poor section of London with his mother, Joanna, becomes fascinated with the idea that unicorns are real. His neighbor, Mr. Kandinsky, tells him that if he could find a unicorn, he could grant all his neighbor's wishes. One day, Joe finds what he thinks is a real unicorn, but it turns out to be a sickly little goat with only one horn. He spends his only two farthings to buy the kid, hoping that it will grant the wishes of Mr. Kandinsky, the pretty seamstress Sonia, and will bring his father home from South Africa so his mother won't be lonely anymore.