England, 1912. The Winslow family arrives home from church in time for a carefully orchestrated meeting between Arthur Winslow (Nigel Hawthorne), the proud patriarch, and John Watherstone (Aden Gillett), the young man set to marry Arthur's daughter Catherine (Rebecca Pidgeon), an ardent suffragette. As plans are made for their lives together, Arthur, his wife Grace (Gemma Jones), Catherine, her eldest brother Dickie (Matthew Pidgeon), John, and Desmond Curry (Colin Stinton), the family lawyer and Catherine's admirer, drink Madeira in celebration of the union.
Just after the family toasts, Arthur discovers that his youngest son, Ronnie, is back early from the Naval College at Osbourne--dismissed for stealing a five shilling postal note. Arthur asks his son if he is guilty, explaining "If you tell me a lie, I shall know it, because a lie between you and me can't be hidden." Ronnie swears that he is innocent.
Arthur dedicates himself to clearing his son of the charges. After obtaining no satisfaction from the school, he decides to retain the well known attorney, Sir Robert Morton (Jeremy Northam). Since he is a conservative opposed to women's suffrage, Catherine is opposed to hiring Morton. In Sir Robert's chambers Desmond explains their predicament: the legal assumption is that the Admiralty and the Crown can do no wrong and cannot be sued. However, by a matter of grace, such a petition can be granted by the Attorney General, allowing the case to come to court.
As the Members of Parliament argue the case in the House of Lords, Catherine diligently keeps watch from the Women's Gallery. The whole affair is taking its toll on Grace. She explains to Arthur how she misses the tranquility of their once happy home, and how the case is taxing Arthur's health. She questions his motives for proceeding, suggesting pride and self-importance.
Catherine receives a letter from John Watherstone's father, stating if the case continues, he will block the match between Catherine and his son. After reading the letter, Arthur tells Sir Robert, "there is a limit and I have reached it." Later, Catherine and John have a painfully frank discussion of their future, and she agrees that she will drop the case and marry John.
At the House of Lords, the Petition of Right is suddenly granted. When a jubilant Sir Robert asks, "Well, Miss, what are my instructions?" Catherine replies "Aren't they already on the petition? Doesn't it say Let Right Be Done?"
Time has passed. The national interest in the case continues to grow, provoking a media frenzy. John breaks off his engagement to Catherine and marries a more suitable woman, a general's daughter. Arthur's health continues to deteriorate. Grace occupies herself with her courtroom wardrobe. Dickie joins the Territorials amid talk of the coming war.
Desmond proposes to Catherine, knowing that she doesn't love him. When Catherine tells her father that she is taking Desmond's proposal seriously, he responds "better far to live and die an old maid than marry Desmond." The cracks in Catherine's beliefs become more evident as she calls the suffragette effort a "hopeless cause."
Just as the entire family is coming to terms with its doubts about the case and their future, a decision is rendered in the case.