Based on Roger MacDougall’s play, three sons in boarding school plot secretly to accomplish on their own what their father hopes to achieve in his work for world peace.
Young Johnny Hampden (Peter Asher) is reading a paper in bed secretly and switches to a book when his mother Stella Hampden (Yvonne Mitchell) comes in to say goodnight. They can hear men at a peace meeting quarreling. Stella goes back to the other room and hears their accusations of each other. John Hampden (John Mills) is frustrated with the arguing and learns that one man does not plan to come to the next meeting.
Johnny and his older brother Max (Andrew Ray) go back to boarding school after a break and are made to talk with the headmaster Dr. Skillingworth (Alistair Sim).
At home Stella is irritated by John and wishes he spent more time with his sons because he refuses to drive them back to school. She wants to tell him something but starts sorting out which musical records belong to each of them because she is planning to leave. John is surprised and baffled as to why she is leaving, and they discuss their marital problems.
At school Max is caught fighting with Skillingworth’s son Richard, and the headman calls them in for discipline. Max is concerned that Richard is a spy for his father, and Skillingworth denies that is possible.
A student tells the headman a phony story that the boys are trying to help Icarus Hampden escape from his detention in order to cover up a more complicated plot they have involving other schools and the lighting of bonfires as signals.
John and Stella learn that Johnny and Max are in Luxembourg after they left on a plane with a father who knows how to fly. The plane returns to get back before dark, and the boys have to walk to the city.
John and Stella go to the school and argue with Skillingworth about his investigation. The reporter Deeson (Colin Gordon) has been alerted by the boys and comes to write about the story. L. W. Daventry (Jeremy Spenser) and the other boys appear surprised to learn the two boys flew to Luxembourg. Daventry tells Stella that children help hold the family together because he and other boys in boarding school often find that their parents separate.
Stella decides to stay in town near the school, but John says he has to give a speech. When he learns about Icarus flying to Vienna, he decides to stay also. Deeson interviews the parents and writes the story that appears in the next newspaper.
Finally the boys get the signal, ring the bell, and the light the bonfires. They meet at the bonfire, and Daventry gives a paper that Icarus wrote to Stella who asks him to read it. The petition from the boys at the school asks the national leaders meeting in Vienna to realize that these boys are not willing to kill the boys of other schools. Deeson is given the paper and says it will be printed in newspapers around the world. They are very happy and celebrate around the bonfire.