Note: this is a synopsis for the 1970 film and differs in small instances from E. Nesbit's source novel and various television versions.
London, Christmas Day 1904. Two men call on Charles Waterbury (who works for the Foreign Office) and lead him away after a terse discussion. When he fails to return in the next few weeks, his wife announces that she and the children - Roberta (Bobbie), Phyllis and Peter - will be moving to Oakworth Yorkshire "to play at being poor for a while". They move into a cottage called Three Chimneys.
The next morning, the children discover that a nearby field backs onto the railway line. They wave at a passing steam train with their handkerchiefs. A distinguished-looking gentleman waves back. Following the line, the children arrive at Oakworth station where they meet porter Albert Perks.
As winter continues, Mother takes ill in their chilly cottage. Peter steals coal from the station sheds but is caught by Bobbie. Peter protests that trying to keep Mother warm can't be wrong. Bobbie resolves to do something constructive to help. The children paint a large sign on an old bedsheet "LOOK OUT AT THE STATION" and wave it at the 9.15 the next day. When the train stops at Oakworth, Phyllis passes a note to the Old Gentleman.
A hamper of supplies is duly delivered to Three Chimneys and the children thank the Old Gentleman with a similar sign. But when Mother recovers and discovers the provisions were acquired by charity she is furious. The family are nonetheless reconciled for Bobbie's birthday.
One day a ragged man staggers off the train at Oakworth, babbling in French. Mother is called to interpret. He is Russian dissident Szczepansky, , who has escaped the Siberian mines for England to find his family. Mrs Waterbury has Szczepansky convalesce at their home and suggests the children say a prayer "for all prisoners and captives".
One day, the children witness a landslide. Knowing they cannot possibly clear the line before the 11.29 passes through, the girls create warning flags out of their red bloomers. Bobbie stands firm between the rails, waving the red rags as the brakes are slammed on. The train comes to rest just in time.
A ceremony is held at the station to commemorate the children's bravery. The railway Director is the Old Gentleman. Bobbie asks him if he might be able to help Szczepansky. The Director eventually succeeds and Szczepansky leaves for London to be reunited with his family.
The children ask around the town for birthday presents for Perks. He is initially furious, but is touched when the children convince him the gifts are a mark of respect from his fellow townspeople. To say thank you, Perks hands Bobbie some old magazines, but she is later horrified to notice a newspaper headline: announcing her father's conviction and sentence to penal servitude. Knowing he is innocent, Bobbie resolves to rescue him. The next day, she hands a letter to Perks to pass on.
A while later, the children watch grammar school boys hold a 'fox and hounds' paper chase. One of the hounds fails to emerge from the railway tunnel. Investigating, they find their 'hound in a red jersey' with a broken leg. The boy, Jim, is taken to Three Chimneys. When Jim's grandfather comes to visit - it is their Old Gentleman! Bobbie has a private chat with him about her father. He says he had received her letter and has been looking into the case.
Some time later, when the children wave at the passing 9.15, the whole train waves back as if in celebration. At the station, Bobbie is greeted by an overjoyed Perks. A train from London halts and, as the steam clears, Bobbie sees a tall figure on the platform.
Arm in arm, father and daughter walk back to the cottage. Father enters and closes the door as the children leave their parents alone to be reunited.
