Dr Paul Martin leaves his wife, Claire, in London to enjoy a Cornish fishing holiday alone. While in his boat he is pulled underwater by Miranda, a mermaid. Taking him to an underwater cave, she informs him that she intends keeping him as there is a terrible shortage of men below sea. She finally decides to allow him his freedom, on condition that he takes her with him in the guise of a patient, explaining that she has always wanted to visit London. He telephones a boutique and has several extra-long dresses made and sent down in preparation for the trip.
In London, Claire receives a letter from Paul explaining that he will be bringing a patient, who cannot walk, to live with them for three weeks. Shortly after, two large crates of fish arrive.
Paul is met at the railway station by his manservant Charles, and instructs him to take Miranda on a sightseeing tour while he goes on ahead to square things with Claire. Miranda immediately begins flirting with Charles, who tells her he is 'walking out' with Betty, the Martins' maid. But when he returns with Miranda in his arms he is clearly besotted, and Betty jealously argues with him about it.
Claire insists that Paul hire a nurse when she discovers that the patient is young and attractive. Paul rings Nurse Carey, an elderly eccentric nurse with whom he has worked in the past. She arrives and immediately becomes Miranda's confidante and ally: she has always believed in mermaids and is delighted at being proved correct.
Paul and Claire invite Miranda to Covent Garden to see an opera with their newly engaged friends Nigel, an artist, and Isobel, a hat designer. During the interval Nigel remains with Miranda in the box while the others go to the bar, and he willingly agrees to her request that he should paint her portrait. Nurse Carey takes Miranda to Nigel's studio for her first sitting on the pretext of taking her to the museum. When she goes on to the museum alone, Nigel and Miranda kiss.
The following day, Charles drives Miranda to the zoo. While watching the seals being fed, Miranda catches a fish in her mouth, and then talks to the seals in their own language. After relaxing on the grass, Miranda kisses Charles. Later, parked by a lake after a drive, Miranda and Paul kiss. They swim in the lake, and Claire sees them arriving home late with wet clothes.
Claire tells Paul that Miranda is causing trouble, and that she has discovered he had expensive clothes specially made for her while in Cornwall. Miranda gives both Nigel and Charles locks of her hair, and they break off their respective engagements, each unaware of the other's claim to her affections.
Claire ponders Miranda's various eccentricities - she sleeps in a cold bath, drinks salt water, eats raw fish sandwiches and, most horrifying, "never wears panties!" - and suddenly realises that she is a mermaid and is enchanting the men. Nigel appears and tells her that Miranda has given him a lock of her hair as a token and he intends asking her to marry him. Then Charles arrives and announces that he too has decided to propose to Miranda, and has also been given a lock of her hair. Realising they have been duped they each apologise to their fiancées and are taken back.
When Paul returns Claire tells him that she now understands exactly what has been happening, and Paul sheepishly reveals that he too has a lock of Miranda's hair. While Miranda is bathing she overhears Claire trying to convince Paul that they should go public with their discovery. Miranda, whose great-auntie had been pickled and used as a sideshow exhibit, leaves in her wheelchair and jumps in the river. Paul and Claire kiss and make up, and Claire vows never to let him holiday alone again. Miranda sings happily with a half-fish child in her arms. A caption reads: 'Fin'.
