An orphan, Phillip "Pip" Pirrip (Anthony Wager), lives with his shrewish older sister and her kind-hearted blacksmith husband, Joe Gargery (Bernard Miles). One day, Pip runs into an escaped convict, Abel Magwitch (Finlay Currie). Magwitch intimidates the boy into getting him some food and a file for his chains. However, the man is caught when he attacks another escapee he hates and is taken back to prison.
Later, Miss Havisham (Martita Hunt), a rich, aloof spinster arranges to have the boy come to her mansion regularly, to provide her company and to play with a cruel but beautiful teenage girl, Estella (Jean Simmons). Estella mocks Pip's coarse manners at every opportunity, but Pip quickly falls in love with her. Once, he meets one of Miss Havisham's relations, Herbert Pocket (John Forrest), a boy about his age. Pip also bumps into Mr. Jaggers (Francis L. Sullivan), Miss Havisham's lawyer. The visits come to an end when Pip turns 14 and begins his apprenticeship as a blacksmith. Estella leaves also, to learn to become a lady.
Six years later, Mr. Jaggers shows up and tells him that a mysterious benefactor has offered to turn Pip (played as an adult by John Mills) into a gentleman, one with "great expectations". Pip naturally assumes that it is Miss Havisham. He is taken to London where Mr. Jaggers arranges for Pip to stay with a grownup Herbert Pocket, who will teach him how to behave like a gentleman. From Herbert, Pip learns that Miss Havisham is embittered and her mind warped at being left at the altar many years ago; she is determined to avenge herself against all men, and Estella is to be her instrument of vengeance, a heartless creation to break men's hearts. Pip refuses to believe it.
After Pip turns 21, a visit from Joe Gargery shows that Pip has become a snob, as evidenced by his ill-concealed irritation at Joe's clumsy manners. Joe brings a request from Miss Havisham to see her. There he is delighted to be reunited with Estella (Valerie Hobson), though she warns him point-blank, "You must know, Pip, I have no heart," but Pip does not believe it. She is about to enter London society. Estella and Pip spend much time together, though she flirts with many men, especially the unpopular, though wealthy and well-born Bentley Drummle, much to Pip's disgust. However, she confesses to Pip that though she flirts with Drummle, she has absolutely no feelings for him.
Pip receives another visitor from the past. Magwitch appears and tells Pip that he is his patron, not Miss Havisham. Mr. Jaggers confirms the news, if indirectly, inasmuch as Magwitch has apparently been transported to Australia (where he made the fortune that has paid for Pip's refinement) and will be hanged if found in England. When Jagger's assistant, Mr. Wemmick, warns Pip that an old enemy (the other escapee at the beginning of the film) knows that Magwitch is in London, Pip makes preparations to smuggle the old man onto a packet boat and accompany him to the Continent.
He goes to bid farewell to Estella and finds her with Miss Havisham. When pressed, she tells Pip that she is going to marry (and torment) Drummle. Pip affirms to Miss Havisham that she has gotten her revenge, at least on him; he loves Estella without hope. For the first time, Miss Havisham regrets her actions. After he leaves, a piece of coal dislodged from the fireplace sets her dress (her wedding dress) on fire. Pip hears her screams and smothers the flames with a rotting tablecloth, but is unable to save Miss Havisham.
When Pip, Herbert and Magwitch row out to the packet boat, they are intercepted by the waiting police, tipped off by Magwitch's great enemy. Magwitch grapples with his nemesis, who is struck and killed by the vessel. Magwitch is seriously injured. The old man had previously spoken to Pip of his lost daughter. Pip's suspicions are aroused and then confirmed by Mr. Jaggers: she is Estella. Pip visits the dying Magwitch and tells him of her fate, and that he, Pip, is in love with her. Magwitch passes away, a contented man.
Stricken by illness and with his expectations gone, Pip is taken home and nursed back to health by Joe Gargery. When he recovers, he revisits Miss Havisham's deserted house. There he finds Estella. When Mr. Jaggers told Drummle of her true parentage, he broke off the engagement. She inherited the house. Learning that Estella plans to live in seclusion just like her mentor, the alarmed Pip tears down the curtains and forces open the boarded-up windows; for the first time in years, sunlight lights the room, revealing cobwebs and dust. Pip forces Estella to look at it and tells her that he has never stopped loving her. After hesitating, she embraces him and they leave the house.