On the busy streets of Oxford, Rebecca Howard, Susannah York, a model and former Oxford mathematics student, is sprinting to attend the ceremony where the Prime Minister is to be awarded an honorary degree when she collides with the aloof Sebastian, Dirk Bogarde. After a sharp insult, Becky is strangely intrigued by him and follows him to the ceremony.
Back at the event, Becky proves resilient and quick-witted, spelling her own name backwards during a particularly tough interview, and Sebastian hands her a phone number inviting her to call if she wants an unspecified job with the British civil service.
Becky soon learns that the position is with the all-female decoding office of British Intelligence that Sebastian directs, a unit dedicated to deciphering codes used by secret agents and foreign spies. As she settles into this demanding new role, she becomes captivated by the enigmatic director, whose private life remains a guarded mystery.
Within the hierarchy, Gen. Phillips, head of security, grows suspicious of Elsa Shahn, a longtime senior decoder with left-wing leanings. Elsa Shahn, Lilli Palmer, is seen as a potential security risk, but Sebastian argues for retaining her because of the crucial value she provides to the operation. Becky, observing the tension, becomes entangled in the office dynamics and the personal allure surrounding the director.
Becky moves closer to Sebastian, and their professional relationship blooms into romance, even as he leaves his girlfriend, Carol Fancy, Janet Munro, a faded pop singer who carries her own burdens and ambitions. The era’s swinging mood shades the workplace as Becky grows frustrated with Sebastian’s single‑minded devotion to his work, which strains their relationship and his living situation.
The plot thickens as Shahn’s political ties come under scrutiny, and a security breach emerges to threaten the entire operation. When Phillips confronts the issue and Becky accidentally reveals their relationship to the office, Sebastian resigns, ends things with Becky, and returns to Oxford, leaving the decoding team to pick up the pieces. Months pass, and the Head of Intelligence asks Sebastian to come back temporarily because the Americans want his help deciphering signals from a Russian spy satellite, a request he agrees to only if Shahn can receive a full pension.
In the pursuit of Becky, who has also stepped away from the decoding department, Sebastian encounters Carol at her apartment. He is drugged with LSD and lured to the top of the building by Toby, Ronald Fraser, who is secretly a foreign agent and Carol’s lover. Just as Toby engineers a deadly ploy to push Sebastian toward a fatal leap, General Phillips intervenes, saving him and arresting Toby.
Sebastian finally locates Becky, and the truth comes to light: he is the father of her newborn baby, and his love for her remains. A clue to the Soviet signal emerges from the sound of the baby’s rattle, and Becky helps Sebastian pivot to decoding the signal in her own living room, bridging love, duty, and ingenuity in a tense, clever finale.
