Slim and Tubby are American cops in London to study police tactics. They wind up in jail and are bailed out by Dr. Jekyll. Jekyll has been murdering fellow doctors who laugh at his experiments. He has more murders in mind. At one point the serum that turns Jekyll into the murderous Hyde gets injected into Tubby.

In Hyde Park, London, at the turn of the century, a string of murders by a wolfman-like monster is capped off by the death of a prominent physicist, whose body is discovered by American reporter Bruce Adams. The next day, Bruce hears dancer Vicky Edwards lead a suffragette meeting in the park, and asks for a private interview. When he punches a heckler, a riot breaks out, and bumbling bobbies Slim and Tubby show up to try to keep the peace. Their failure, however, leads the police inspector to fire them. Later, Bruce and all the suffragettes are bailed out of jail by Vicki's guardian, leading scientist Dr. Henry Jekyll, who secretly loves his ward. Bruce finagles a ride with Jekyll and Vicky, quickly sparking the doctor's jealousy. In the carriage, Jekyll explains to Bruce his desire to gain control over man's dual nature, in order to stamp out evil and violence. As Bruce accompanies Vicky to the dance hall where she works, a dejected Jekyll goes home and enters his secret laboratory, where his mute assistant Batley awaits. There, Jekyll, who has been testing a serum which produces the manifestation of his dual nature, a monster named Mr. Hyde, laments that Hyde killed the physicist. Jekyll almost vows not to use the serum again until he has perfected it, but then recalls his desire to eliminate his new rival for Vicky's affections. He injects himself, transforms into Mr. Hyde, and goes to the dance hall, where he watches through a window as Vicky and Bruce kiss. Just then, Slim and Tubby pass by and see Hyde scaling the wall of the theater. Assuming he is a burglar and hoping to win back their jobs, the two chase him into the building and begin searching the dressing rooms. After barely escaping Hyde's clutches several times, Tubby finally notices the monster, but fails to capture him. Luckily, Bruce and Slim see Hyde in the hallway and chase him through a skylight. All three pursue him over the rooftops, but lose him when Tubby slips and dangles off a clothesline. Tubby, left behind by Bruce and Slim, unwittingly enters the same wax museum in which the monster is hiding. There, he is terrified by every statue and screams until Slim hears and runs in. Learning that Hyde is in the museum, Slim races to the inspector, leaving Tubby to trap the monster in a cell. By the time the inspector arrives, however, the serum has worn off, and Tubby is castigated for imprisoning Dr. Jekyll. Jekyll then invites Slim and Tubby to his house and asks them to stay the night. Tubby, terrified, wakes in the night and attempts to escape, but is so frightened when he sees Batley that he accidentally rushes into the secret laboratory. After his bumbling wakes Slim, Jekyll invites them both to tour his lab, and Tubby grabs a bottle of serum and drinks it, thinking it is water. He then leaves, followed by Slim, who does not notice when Tubby transforms into a giant mouse. Each man, realizing the metamorphosis at the same time, faints, and when they wake, Tubby is himself again. They visit the inspector to inform him of Jekyll's evil experiments, but are proclaimed insane and thrown out. The next day, they tell their story to Vicky and Bruce, who insist on confronting Jekyll themselves. He willingly shows them his laboratory, which by now has been cleaned out. While Bruce and Vicky apologize, Slim finds a bottle of spirits he believes to be the mouse potion and urges Tubby to drink until he is completely inebriated. Upstairs, Bruce asks Jekyll for Vicky's hand in marriage, and although the doctor agrees, he grabs Vicky as soon as Bruce leaves and declares that no one will have her but himself. He prepares a needle with which to turn Bruce into a monster so he can kill him legally, but when Vicky fights him, he accidentally injects himself and turns into Hyde before her eyes. Her screams alert Batley, Tubby, Slim and Bruce, who is just outside, and all four rush into the library. There, while Bruce battles Hyde, Batley repeatedly pushes Tubby into the serum-filled needle until he becomes a monster identical to Hyde. Both he and Hyde escape into the park, and soon the whole police force is after both monsters. Finally, Slim chases Tubby onto a rooftop just as Bruce follows Hyde onto the same roof. All four hide around one chimney until Slim manages to attack Tubby. Hyde, however, flees to his house and attacks Vicky. Bruce, who has also gone there in the hope that Jekyll would return, breaks into the house and fights Hyde until the monster jumps out of the window to his death. As the citizens surround him, the monster's face transforms back into Jekyll's. Meanwhile, Slim and four policemen have brought Tubby to the inspector's office, and a struggling, monstrous Tubby bites all of the policemen. They knock him out, and when he converts back into his human self, the two pals turn around, only to find that the five bitten lawmen have mutated into monsters.