Southern England, the late 1950s. Having threatened to expose the occultist Karswell, scientist Professor Harrington dies violently, having been pursued by a monstrous demon invoked by Karswell. As his car has been hit a power line, the authorities conclude that Harrington has been killed by electrocution.

American psychologist Dr John Holden visits the UK, to attend a convention with Harrington, where the latter had been due to discuss Karswell's 'devil cult'. Perusing Harrington's papers, Holden and some other fellow scientists find prints of fire demons from an ancient manuscript; these bear a marked resemblance to a sketch done by a member of the magician's cult, since arrested for murder and now in a state of catatonic shock. Holden receives an unexpected telephone call from Karswell, who asks him to abandon his investigation.

Although sceptical of the supernatural, Holden is intrigued enough to visit the British Museum to look at the volume from which the demon prints were copied. This proves to have gone missing. Enter Karswell, who offers to loan Holden a copy. Knocking over Holden's papers, he secretly passes him a parchment invoking a fire demon. Unaware of this transaction, Holden nonetheless immediately begins to feel unwell. Looking at Karswell's visiting card, he briefly sees the words "Henry Harrington, allowed two weeks", before they vanish.

Having met Harrington's niece Joanna on his flight to England, Holden encounters her again at the professor's funeral. She informs him that all the pages in her uncle's diary for the ten days leading to his death have been ripped out.

Holden visits Karswell's country house with Joanna, who is equally intrigued but less sceptical. The magician is hosting a party for local children, and is dressed as 'Bobo the Magnificent', a conjurer with clown's makeup and red nose. Karswell summons up a storm to convince Holden of his powers, and informs him that, having received the parchment, he is cursed to die at the hands the demon, either at ten o'clock four days hence, or as soon as the paper leaves his grasp. At dinner with Joanna later that evening, the parchment flies from Holden's wallet towards the fire, but he is able to retrieve it.

Following a visit to Stonehenge in an attempt to decipher the parchment's runic symbols, Holden pays a call on the relatives of Karswell's catatonic disciple, Rand Hobart.  They are less than helpful, protective of Hobart and seemingly involved in the cult in some way. Holden and Joanna then grudgingly attends a séance arranged by Karswell's mother and a jolly medium, Mr Meek. Joanna is convinced she hears Meek speak with the voice of her late uncle, reliving his death at the hands of the demon.

Breaking into Karswell's mansion to examine his manuscript, Holden is attacked first by a leopard summoned by the magician, then by a strange cloudy presence in the woods. Pursued by huge phantom footfalls, Holden runs for his life to Joanna's waiting car.

Undeterred but gradually losing his scepticism, Holden attends the science convention, where the catatonic Rand Hobart is awakened from his trance via hypnosis. Hobart claims to have taken the blame for a previous murder, so as not to expose the devil cult. Reliving a visitation of the fire demon, he proceeds to run amok and jumps to his death from a window. Pursued by the police, Holden boards a train, finding Karswell on board with Joanna, who he has abducted.

As the hour of ten swiftly approaches, Karswell is clearly anxious that Holden will attempt to surreptitiously slip the parchment to him, reverting the curse of the demon back onto he who summoned it. As the police arrive, Holden puts the parchment into Karswell's coat, passing it first to the police then to the magician, who unwittingly accepts it. The paper then flies from from Karswell's grasp, causing him to chase desperately after it down a railway track. The parchment combusts on a railway line, and the fire demon appears. The terrified magician is tossed into the air, then trampled to death. Onlookers assume that Karswell has been killed by an oncoming train.