Divorced architect Paul Lindon travels by train with his new French wife Nichole (at 24, half his age) from Paris to London where she will meet his 'wild child' 16 year old art student daughter Jenny, into beat music and jazz, for the first time. On arrival, Paul's house is cold and uninviting, and he shows Nichole a model, displayed in a coffin-like case, of the futuristic 'City 2000', which is planned for South America. At their first meeting Jenny is cool towards Nichole and to upset her, displays a book on jazz which features a photo of her mother. After bedtime Jenny sneaks out to meet her friends at Soho's 'Off Beat' coffee bar for cool chat and jive in the basement.
The next day, Nichole visits St Martin's School of Art to see Jenny as she had agreed, and is told to go to the nearby 'Off Beat' coffee bar in Soho. There she meets Jenny and her 'beat' friends, and on leaving, is recognised by 'The Duchess', who regularly meets girls there for auditions at a nearby strip club 'Les Girls', where she works. The 'beat' gang are puzzled as to why the outwardly respectable Nichole should be known to the disreputable 'Duchess'. Ever-curious, Jenny visits 'Les Girls' and is told by 'Duchess' (real name, Greta) that Nicole used to work as a stripper (and implied involvement in the vice trade) when they were both in Paris. Greta also has an on-going relationship with the reptilian club manager Kenny, who invites Jenny to his office and suggests that she should work for him at 'Les Girls'.
Returning home at 3am, Jenny is met by Paul and she explains the 'beat' lifestyle to her 'square' dad, who finds it totally incomprehensible. Nichole decides to visit 'Les Girls' to confront the secret from her past, and meets Greta. She also warns Kenny to keep away from Jenny as she is 'under age'. Meanwhile, Jenny is at an underground 'beat' venue in Chislehurst caves, and she invites the gang back to dad's house for follow up party. En route, the 'beats' are in search of 'kicks' by racing their cars and playing a dangerous game of 'chicken' on a railway track.
At the party, Jenny starts to strip, but is interrupted by Nichole, who is trying to sleep upstairs. Paul enters and orders the gang out of house. Nichole admits her past to Paul - that she was more than a 'ballet dancer' with Greta in Paris.
Jenny makes another visit to 'Les Girls', and Kenny shows her two air tickets to Paris for them both, suggesting they leave the country together. While a stripper is performing, there is a scream from the office and Kenny falls to the floor, a knife in his back. Soon the police arrive, together with a frantic Paul and Nichole, in search of Jenny. Greta emerges from behind a curtain in the office, revealing that it was she who, in a fit of jealousy, wielded the knife that killed Kenny. Paul embraces Nichole and Jenny and, now united as a family, they walk away, turning their back on vice and Soho.
