London, the early 1950s. Christine Garland confides in her friend, Lily, her concerns about her two-year-old daughter, Mandy, who has not yet started to speak. Later, Christine and her husband Harry realise Mandy may be deaf. A specialist confirms she has been profoundly deaf since birth. He tells Christine that Mandy's condition is untreatable and she is likely to remain dumb.
Harry visits a school for the deaf in Manchester, but dislikes it, and they decide to educate Mandy at home. Lacking space, they move in with Harry's parents, Emily, who is delighted to have a child in the house, and Fred, who is preoccupied with his postal chess game.
Five years later. The family dog runs out into the road and Mandy follows, and is almost hit by a passing lorry. The driver shouts at Mandy and she runs home in tears. Christine tries to comfort her, but is desperate that Mandy cannot communicate what is wrong.
At Lily's suggestion, Christine visits the school which Harry had previously rejected. The headmaster, Mr Searle, treats her rudely, but she is impressed by the the evident success of his methods. Later, she is introduced to Jane Ellis, semi-retired founder of the school. When Christine realises that Miss Ellis is herself deaf, she becomes convinced that the school can help Mandy.
Christine tries to convince Harry to allow Mandy to attend the school, but he and Emily are both opposed. They take Mandy to the park, where she meets a young boy and girl, who take her ball and force her to play piggy-in-the-middle. Frustrated, Mandy attacks the boy, and is dragged off by his mother, who screams that Mandy is mad. Back at home, Christine and Harry argue. When Christine accuses Harry of selfishness, he hits her. She takes Mandy and leaves.
When Christine arrives at the school with Mandy, Searle is in a board meeting, where he clashes with one of the governors, Ackland. Christine leaves Mandy with a young teacher, Miss Stockton. But Mandy doesn't adjust well to the school, refuses food and wakes up crying in the night.
Searle is ready to accept defeat, but Christine suggests that she takes lodgings nearby so that Mandy can become a day pupil. Meanwhile, Harry has approached a solicitor, who suggests trying to pressurise Searle through Ackland. When Ackland raises the issue with Searle, the headteacher is dismissive. Later, when his secretary suggests that Searle and Christine might be having an affair, Ackland enlists an employee, Davey, to spy on them.
Miss Stockton successfully coaches Mandy to sound the letter 'p'. Encouraged, Christine writes to Harry, who agrees to visit. They have an emotional reunion, but the next morning Harry suggests they all return to London and find Mandy a local school. When Searle appears, Mandy runs to him, and Harry leaves, furious.
To speed up progress, Searle offers to coach Mandy in the evenings. Meanwhile, Davey speaks to the landlady. When, with Searle's help, Mandy has a breakthrough and says her first word - 'Mummy' - Christine is delighted and kisses Searle. But the landlady sees them, and tells Davey.
Later, Miss Ellis warns Searle that Ackland is digging for dirt, and advises him to break off the home tuition. By now, however, Harry has learned from his solicitor of the 'affair', and heads for Manchester. He arrives at Christine's flat to find her out celebrating with Searle, and Mandy with a babysitter. When Christine returns, he confronts her and Searle, who protests innocence. Searle leaves, and Christine tries to demonstrate Mandy's progress, but Mandy is upset and cannot speak. Furious, Harry takes Mandy and leaves for London.
Christine and Searle follow, and Searle tries to persuade Harry he is being used by Ackland. While they argue, Mandy wanders the house and finds Fred, who is absorbed in his chess, until Mandy begins to make sounds. Startled, Fred confronts Harry and asks him if he really believes Christine has been unfaithful. Harry admits he doesn't.
Meanwhile, Mandy wanders into the yard, where a group of children are playing. When asked, she manages to say her name, and is invited to join their game, as Christine and Harry look on.