After successful pianist Lissa Campbell is diagnosed with a terminal heart defect, she vows to make her last months worth living. Checking into a Cornish hotel, she meets retired Yorkshire businessman Tom Tanner. He senses she's unhappy, but doesn't probe further.
On a clifftop walk, Lissa meets former RAF pilot Kit Firth. He's found a molybdenum rock, and she is fascinated by the waves and the seagulls. Later, when Tom shows her the hotel's grand piano, she absorbs herself in creating a new piece of music, inspired by her feelings about the encounter.
Kit introduces Lissa to his old friend Judy Martin, who is producing The Tempest in an amphitheatre overlooking the sea. Kit offers to show Tom the molybdenum (which could be profitably mined) in exchange for funding Judy's play. Tom is unimpressed by Kit's pitch, but is transfixed by Judy, as her eyes remind him of his late wife's.
Kit confides to Judy that he can't get involved with Lissa because he's going blind. Lissa forces Kit to talk about his feelings, and he says he might not feel the same about her in six months. Laughing, Lissa says she's the one who'll walk out on him, and they agree to abandon each other without any fuss when the time comes, settling it with a handshake through the local "bargain stone".
Tom offers Kit the job of setting up the molybdenum mine, but Kit turns it down. Tom calls him a coward and says that he'll do it himself. Later, Lissa challenges Kit, asking him whether he refused the job because he was afraid. When Kit replies that it's not a question of fear, merely of not caring, Lissa calls him selfish.
Judy encourages Kit to tell Lissa about his feelings for her, but he refuses. They are interrupted by news that there's been a disaster in the mine and that a group of men, including Tom, are trapped.
While Judy and Lissa wait anxiously, Kit goes down the mine to help, but is trapped with Tom and the miners when the ceiling collapses. Kit finds a way out, but it involves a large amount of dynamite. His gamble succeeds, and they are all rescued.
Tom and Lissa agree they misjudged Kit - he clearly isn't a coward, but they still don't know what makes him tick. Lissa visits him and finds him reading braille. He tells Lissa that thanks to an accident in the RAF he'll go blind within three months - he turned down Tom's job because he wanted to spend the time above ground. There is an operation available, but it's a hundred-to-one shot, and Judy advised him not to take it.
Lissa goes to Judy and demands that she let Kit have the operation. In a heated exchange, Judy reveals her secret love for Kit. They strike a deal: if the operation is a success, Lissa will relinquish her claim to Kit.
At the first night of The Tempest, a nervous Judy refuses to perform until she hears the result of the operation. Lissa pacifies the restless audience by performing her now-completed piece. At the end, she is so overcome with emotion that she faints. When she comes round, she hears that the operation was a success. She tells Judy that she'll keep her part of the bargain, and reveals her secret.
Visiting Kit in hospital, Lissa bids him farewell, saying that she's going on a tour of North Africa to entertain the troops and that she's not sure when she'll be back.
Kit proposes to Judy at a party, and she accepts. While trying to find some dance music on the radio, Kit accidentally tunes into a radio broadcast by Lissa. He switches it off quickly, but Judy sees his reaction and realises that he's still in love with her.
At the Royal Albert Hall, Lissa performs a fully orchestrated concerto version of her piece, and afterwards finds Kit and Judy waiting in the wings. Lissa tells Kit her secret, and says that this means they can never be together. Kit dismisses her concerns by saying that any amount of happiness, no matter how small, is always worth grasping. Kit and Lissa embrace.
