Dolly Messiter runs into an acquaintance, Laura, in a railway station's refreshment room. Laura introduces her companion Alec, a GP. He leaves to catch his train. Dolly returns from the counter to find that Laura has disappeared. When Laura returns, she seems unwell.
Laura is still upset and unhappy when she reaches home, her husband and two children. She starts to cry. Husband Fred takes her into the 'library', and they sit companionably. He does the Times crossword while Laura sews. She listens to Rachmaninov and, in her mind, recounts her story to Fred.
She remembers an earlier occasion at the station. She gets something in her eye when the express roars through. The buffet staff try to help, but a fellow traveler, a doctor, removes the grit from her eye.
In town again the following week, she bumps into the doctor, and then again the week after that. Later, she sees him at the Kardomah café. He joins her table as the place is full. She discovers that he too comes into town every Thursday, to work at the hospital. He is married, with a family. They decide to go to the cinema.
Back at the station buffet, Alec tells Laura about his love for medicine and his ambitions. She is beguiled by his boyish enthusiasm. He persuades her to meet him the following Thursday, although she feels guilty. Reaching home, she finds her son has been knocked down by a car and is concussed, but otherwise all right.
Relieved, Fred and Laura plan their son's future, by the living room fire. Safe in this cosy domesticity, Laura tells Fred about meeting Alec, but he is doing the Times crossword and not really listening. Laura begins to laugh, rather hysterically.
Although now determined not to spend more time with Alec, Laura feels it would be rude not to meet him as planned, but he doesn't turn up. She sees him at the station, and he explains that he couldn't get away. She agrees to meet the following Thursday. They leave the cinema early, then take a boat out on the lake. Alec falls in the water, and they dry off in the boat shed. As they drink their tea they admit that they are falling in love. At the station, Alec steals a kiss in the subway between the platforms.
At home, Laura dreams of a glamorous life with Alec, travelling from country to country. She lies to Fred about how she spent her day, and has to ask a friend to cover up for her.
The next Thursday she meets Alec for lunch in a hotel, but two friends of hers see them together. Alec takes her out for the afternoon in a car he has borrowed from a friend. At the station that evening, he tells her he will miss his train and stay the night at a friend's empty flat. Knowing that he wants her to join him there, Laura runs off in confusion, but changes her mind and goes to the flat. Alec's friend, Stephen, returns unexpectedly almost as soon as she arrives, and she hides. Stephen sees her things and confronts Alec angrily, demanding his spare key back.
Laura runs off, through the rain-soaked streets. She telephones Fred and invents an excuse for being home late. After wandering the town for three hours, she goes to the station in time for the last train. Alec finds her in the buffet. She tells him they must stop seeing each other; it is making her feel too guilty and ashamed. On the platform, they agree to meet one last time the next Thursday. Alec says he will accept a job he has been offered in South Africa.
The following week they drive out into the country, silently revisiting places where they were happy. They spend their last few minutes together at a table in the buffet, but are interrupted by Dolly Messiter. Alec catches his train. Laura hears the express coming through and runs out on to the platform, where, briefly, she considers throwing herself under it. But she cannot bring herself to do it, and goes back home to Fred and the children.
