Autumn 1912, Arthur Winslow has retired from the bank. His wife Grace greets him at home. He scolds his 19-year-old son Dickie, an Oxford student, and complains that his 12-year-old brother Ronnie, accepted for the Royal Naval College at Osborne, sets a better example. John Watherstone, son of Colonel Watherstone, visits Arthur's daughter Catherine, who is interested in the Suffragette movement.

Ronnie leaves for Osborne. Letters home suggest he is doing well, but, unknown to the family, he arrives home two days early. He opens a letter meant for his father and hides in the garden. Arthur approves John's proposal of marriage to Catherine and John tells Catherine of his success. Ronnie enters and shows Catherine the letter. Upstairs, Dickie asks him what he has done. He has been accused of stealing and expelled from Naval College, but protests his innocence. Grace reads the letter to Arthur, describing the theft of a five shilling postal order from a cadet, and requesting Arthur withdraw his son from the college. Arthur twice asks Ronnie whether he committed the crime. When Ronnie replies he did not, Arthur believes him. Arthur asks the college to take Ronnie back and to reveal their evidence, but they refuse.

Catherine introduces John to Desmond Curry, the family's solicitor, who loves Catherine. Arthur asks Desmond to draft a letter to the Admiralty, which he then visits and asks for Ronnie to be given a civil trial. This is refused because it could set a dangerous precedent. Arthur visits his MP, Mr. Hamilton, pressing for an inquiry. The newspapers begin to report the affair and the fame of the Winslow Boy spreads.

The famous KC Sir Robert Morton questions Ronnie about the day of the theft to decide if he will take the case. Ronnie explains he withdrew 15/6 from the college bank and stored it in his locker, before asking permission to visit the Post Office. He retrieved his money, went to the Post Office, and bought a postal order for 15/6. Later he discovered a postal order for five shillings had been stolen from another cadet's locker. Ronnie was summoned by the college authorities who asked the Post Mistress to identify the boy. She couldn't be sure, but said the boy who bought an order for 15/6 was the same boy who cashed the five-shilling order. Ronnie was then asked to write the cadet's name, and this was compared with the signature on the order. A handwriting specialist confirmed it was the same hand. Ronnie was expelled ten days later. Morton discovers that Ronnie had practiced the boy's signature, but believes he is innocent and takes the case.

Arthur tells Dickie he cannot keep him at Oxford due to the case expenses. Catherine receives a letter from John's father saying he will try to prevent their marriage. Morton makes a convincing speech in the House of Commons, resulting in a Petition of Right being granted, enabling the case to be fought in the courts.

Meanwhile, Arthur considers dropping the case due to adverse effects on his family, but learning of Morton's success he asks Catherine to decide. She wishes to continue, thus jeopardising her engagement to John, who cannot afford to lose his allowance from his father.

The court case begins. Catherine learns of John's engagement to another woman. Ronnie is questioned in court. Arthur is becoming increasingly unwell. Morton cross-examines Captain Flower from Osborne, and handwriting expert Mr. Ridgeley Pierce. The Post Mistress is called to stand.

Desmond proposes to Catherine, and reveals Morton sacrificed the post of Lord Chief Justice to continue with the case. Arthur advises Catherine not to marry Desmond, and she reveals that she misjudged Morton. Violet, the maid, tells Arthur and Catherine that the case is won. Morton arrives and reads the Attorney General's statement finding Ronnie innocent. Arthur and Ronnie meet the press.

Morton explains to Catherine that the Post Mistress was discredited as a witness. He is feeling unwell. Catherine reveals she knows of his sacrifice. When Morton leaves, Catherine says she will probably not see him again. His reply suggests a growing romantic attachment between them.