Returning by ferry from a holiday in Ireland, unsuccessful songwriter Peter Weston shares a cabin with a drunken Irishman who disembarks just before boarding, leaving Peter in charge of his pet alligator, named Daisy. Fellow passenger Moira O'Shannon catches Peter attempting to push Daisy overboard and insists that he treat her humanely. Although she works at the London Zoo, she says that they have enough alligators.
Peter and Moira drive back to London together and become better acquainted after stopping to let Daisy swim in a river. However, both are engaged, Peter to Vanessa, the daughter of newspaper magnate Sir James Colebrook, and Moira to Albert, a missionary.
Returning to his parents' house, Peter discovers that his grandfather, a former general with a pathological hatred of 'muggers' (Indian crocodiles) is staying there too. Although Peter attempts to hide Daisy in the bath, she is quickly discovered. An uneasy truce is reached, on condition that Peter gets rid of her as soon as possible.
He tries the police station, which suggests the pet shop, but its eccentric owner insists that Daisy is devoted to Peter and refuses to take her. Reluctantly, he takes her to work at Harker's music showroom. Vanessa visits him to say that her father wants to hold an engagement party at the weekend and meet Peter's family. After she leaves, a customer tries out one of the pianos, only to discover Daisy hidden inside.
Peter tells Moira that he's been fired and that he proposes to abandon Daisy in the Regent's Park lake. He does so that night, but guilt makes sleep impossible, so he goes back the following morning, to find Moira looking for her too. They fail to find her, and Peter dejectedly returns home... but Daisy has preceded him. He rings Moira with the news, and she agrees to look after Daisy that weekend.
Vanessa persuades her father to arrange an audience with Denmark Street song publisher Irving J. Rosenbloom. He has to take Daisy along too, but Rosenbloom is thrilled to meet her, improvising two songs on the spot ('Crocodile Tears' and 'The Crocodile Walk'), both of which he credits to Peter.
On the day of the party, Vanessa turns up before Moira, so Peter has no choice other than to pack the case containing Daisy in with the rest of the luggage. In the vast Colebrook Manor, they meet the eccentric Sir James. Finally safe in his own room, Peter lets Daisy out to give her a bath. He then puts her back in his room and has a bath himself. He returns to find that she's eaten most of the lavish meal intended for him and Vanessa, though he manages to hide the evidence (and Daisy) before she returns.
The guests dance to 'Crocodile Tears' while Sir James interrogates the Westons as to their financial position. One of the butlers (who grew up in Brazil, and consequently loves alligators) finds Daisy in Peter's drawer and takes her out for a walk, before tying her to some stone railings. She breaks the leash and wanders amongst the guests. In the ensuing panic, Vanessa is astonished to see Peter rescuing Daisy and treating her affectionately.
Sir James summons Peter to his office and says that he refuses to let his daughter marry a lunatic. Shortly afterwards, he changes his mind, deciding that if his paper campaigns to establish alligators as acceptable British pets, the marriage might work. A lavish fête and alligator competition is arranged in the grounds of Colebrook Manor, attended by celebrities and newsreel cameramen. Peter bumps into Moira, who has brought Nelson, the zoo alligator, to whom Daisy takes a shine. She has also brought Albert, who has a similar effect on Vanessa.
All the alligators head for the lake, and when Sir James mounts a rickety wooden bridge to announce the winner (Daisy, predetermined), the weight of the crowd causes it to collapse. Albert rescues Vanessa, and Moira reveals that he's actually her brother: she only pretends to be his fiancée in order to stave off unwanted attention. With Vanessa's blessing, Peter and Moira get engaged, and decide that Daisy can live in the zoo... with Nelson.
