Liverpool, 1962. Yee Mah emigrated from Hong Kong in the 1920s to establish a laundry, now run by her nephew Jack Su and his English wife Rita, together with Jack's sister Peggy, who moved to Britain after her mother's death. Peggy receives a letter from her father Jerry, announcing that he has arranged for her to marry her cousin Gilbert. Yee Mah advises her to follow her heart rather than her father's wishes, and offers her advice about finding and keeping men.
Late for a restaurant meal, Peggy collides with one of the waiters, David. Entranced by her knowledge of cleaning techniques, he asks her out on a date. Yee Mah advises her to develop an interest in football, and she gets specific advice from Jack's friend Terry, the delivery man. While helping Peggy prepare for her date, Rita reminisces about Brian Hardcastle, her first love.
Peggy is intimidated by the elaborate décor of the tearooms. She is unused to eating with a knife and fork, and attracts raised eyebrows when she asks the waiter for some soy sauce. Discussing football, she ends up gabbling, and finally they each insist on paying the bill.
Peggy and Jack's family arrives - Jerry, his much younger second wife Jackie, and the clumsy Gilbert. Rita tries to have a conversation with Jerry, unaware that Jackie is deliberately mistranslating in order to secure them Jack and Rita's bedroom. Gilbert offers Peggy crushed and melted chocolates.
Jack tries to teach Gilbert laundry basics, but he is unnerved by the presence of female underwear. A woman hands Peggy a blue dress for cleaning, and stresses its high cost. Peggy writes her name in Chinese as 'Mrs Fusspot'. The family go to the cinema, where Gilbert fails to seduce Peggy.
David asks Peggy to a dance. Rita encounters Jack and Jackie together and refuses to speak to him. Rita, Jackie, Peggy and Terry go to a dance class. Peggy and Terry dance together, while Rita takes a shine to the teacher - who turns out to be her old flame Brian. When the music stops, Jackie notices that Rita and Brian don't immediately separate.
Peggy wears the blue dress to the dance, but finds that it's rock'n'roll rather than ballroom dancing, and, worse, Mrs Fusspot is there. Instead of going in, she walks home despondently.
David takes Peggy out for a drive, while Jerry urges her to spend more time with Gilbert. When Gilbert is put in charge of the soap and bleach, the laundry room fills up with suds, ruining Rita's favourite dress. At tea, Peggy blurts out that she doesn't want to marry Gilbert. A furious row is only resolved when Gilbert tells Jerry that he doesn't want to marry Peggy either.
Terry brings a portable record player round to encourage Peggy to practice dancing with him - she is hesitant, but quickly gets into the swing of things. Brian tries to rekindle his romance with Rita. David rings Peggy to say that his father has given him two restaurants, and he can afford to marry her. Terry proposes shortly afterwards, but she has to turn him down.
After Yee Mah has had a private chat, Jerry approves the marriage. Gilbert becomes surprisingly adept in the laundry, improvising a dance routine involving the boiler and various dresses. Rita goes to see Brian, but finds him dancing with Jackie. Later, she refuses Jackie's request to iron her clothes and threatens to tell Jerry. Jackie orders Gilbert to iron them, and he burns them deliberately.
At the wedding, Gilbert tries to pin a flower to David and ends up drawing blood. The resulting confusion means they go into the church wearing each other's jackets. As the ceremony begins, Gilbert finds a letter in the top pocket - it's from David to 'Sophie', explaining that he's only marrying Peggy ("the peasant") to keep his father happy, as she's Chinese. When this is read out, the wedding collapses in chaos. Peggy makes a defiant speech defending her family.
Jerry and Jackie fly home to Hong Kong. A year later, Peggy has become a successful ballroom dancer, winning prizes in partnership with Gilbert. Terry gives her a pair of high-heeled dancing shoes.
