Two cars stop in a traffic jam in a London street. A man and a woman indicate, and their hands become entangled, with he inadvertently taking her glove. Later that evening, the man (Tom Daly) arrives at a radio station at the last minute and improvises a song about the mystery woman called 'What's Her Name?'
The song becomes a hit, and the family firm of Daly's Music Publishers is in discussion with millionaire American publisher Oliver Berne about a possible merger. Berne goes to Tom's office but Tom, thinking he's a messenger boy, throws a pot of ink at him. Outraged, Berne cancels the deal - and Tom's father disowns him, saying that he'll only take him back once he's found the girl that inspired his only hit.
The mystery woman turns out to be Pamela Berne, who delights in terrorising her staff. The butler threatens to resign along with everyone else. In front of her father, Pamela coquettishly claims that she was acting in everyone's best interests, but she reverts to her old ways behind his back.
Tom visits an old schoolfriend, Harry and sees a photo of Pamela on the piano. Harry is bemused and amused by his claim that "she's the most angelic thing I've ever seen in my life", but confesses that she's his sister. The still ink-stained Berne arrives and is infuriated with Tom - until Harry tells him his intentions, whereupon he offers him cigars, champagne and his blessing.
Tom goes upstairs and asks her to marry him. She throws him down the stairs, following after him to find Tom, Harry and Berne discussing Berne's debts towards Tom and Tom's threat to foreclose because Pamela turned down his offer of marriage. Fooled by this, she changes her mind.
At the church, Pamela arrives on Berne's arm, and is annoyed to find that Tom hasn't turned up. He eventually appears, clad in plus-fours and bearing golf clubs. He apologises, but says he was playing golf and forgot all about the wedding. Afterwards, she refuses to come on the honeymoon, but Tom handcuffs her to him and says that the key is at the hotel and only he knows precisely where.
Pamela causes a car accident when she attempts to powder her face using the hand that's handcuffed to Tom's steering hand. The car a write-off, they walk to the nearest hotel, and while Pamela is loudly complaining Tom strikes a surreptitious deal with the landlord that involves him offering their worst room and just bread, cheese and pickles to eat.
Banished from the room, Tom puts on a record and sings and dances in the courtyard. Pamela watches but is unmoved. The next day, they're given a lift to the station in a rusty old banger. Tom shows Pamela a telegram from her father saying that he's let the family home and gone away to South America, forcing her to go home with Tom.
At Tom's house, they are shown in by a sinister butler who hints that Tom's previous brides met tragic ends. The rest of his family are similarly doom-laden, mad or only recently released from prison. When Pamela flees to her bedroom, normality returns and it's revealed that Tom's "family" are all hired actors. Upstairs, while Tom is engaging in an exaggerated "fight" with his jailbird "brother" to impress Pamela, the phone rings and Pamela answers it - it's the theatrical agency requesting the return of the actors.
Enraged, Pamela comes downstairs and trashes the place. Tom agrees to a divorce and rings a hotel in Brighton to fake a dirty weekend with another woman to be used as justification. But while he's doing this, the house's owner (another friend of Tom's) returns and tells Pamela that he only went to these lengths because he was madly in love with her.
Tom enters the Brighton hotel room to find a semi-clad woman in the darkness. He tells her he can?t go through with the plan because he loves his wife - whereupon Pamela switches on the light to reveal herself. The reconciled couple sing an updated version of 'What's Her Name', in which the song is brought to an emphatic conclusion.