Joe is a young boy who lives with his mother, Joanna, in working-class London. The two reside above the tailor shop of Mr. Kandinsky, who likes to tell Joe stories. When Kandinsky informs Joe that a unicorn can grant wishes, the hopeful lad ends up buying a baby goat with one tiny horn, believing it to be a real unicorn. Undaunted by his rough surroundings, Joe sets about to prove that wishes can come true.

Londoner Harry Fabian is a second-rate con man looking for an angle. After years of putting up with Harry's schemes, his girlfriend, Mary, becomes fed up when he taps her for yet another loan.