The novel opens with mystery author Harriet Vane on trial for the murder of her former lover, Phillip Boyes: a writer with strong views on atheism, anarchy, and free love. Publicly professing to disapprove of marriage, he had persuaded a reluctant Harriet to live with him, only to renounce his principles a year later and to propose. Harriet, outraged at being deceived, had broken off the relationship.

Following the separation, the former couple had met occasionally, and the evidence at trial pointed to Boyes suffering from repeated bouts of gastric illness at around the time that Harriet was buying poisons under assumed names, to demonstrate – so she said – a plot point of her novel then in progress.

Returning from a holiday in North Wales in better health, Boyes had dined with his cousin, the solicitor Norman Urquhart, before going to Harriet's flat to discuss reconciliation, where he had accepted a cup of coffee. That night he was taken fatally ill, apparently with gastritis. Foul play was eventually suspected, and a post-mortem revealed that Boyes had died from acute arsenic poisoning. Apart from Harriet's coffee and the evening meal with his cousin (in which every item had been shared by two or more people), the victim appeared to have taken nothing else that evening.

The trial results in a hung jury. As a unanimous verdict is required, the judge orders a re-trial. Lord Peter Wimsey visits Harriet in prison, declares his conviction of her innocence and promises to catch the real murderer. Wimsey also announces that he wishes to marry her, a suggestion that Harriet politely but firmly declines.

Working against time before the new trial, Wimsey first explores the possibility that Boyes killed himself. Wimsey's friend, Detective Inspector Charles Parker, disproves that theory. The rich great-aunt of the cousins Urquhart and Boyes, Rosanna Wrayburn, is old and senile, and according to Urquhart (who is acting as her family solicitor) when she dies most of her fortune will pass to him, with very little going to Boyes. Wimsey suspects that to be a lie, and sends his enquiry agent Miss Climpson to get hold of Rosanna's original will, which she does in a comic scene exposing the practices of fraudulent mediums. The will in fact names Boyes as principal beneficiary.

Wimsey plants a spy, Miss Joan Murchison, in Urquhart's office where she finds a hidden packet of arsenic. She also discovers that Urquhart had abused his position as Rosanna's solicitor, embezzled her investments, then lost the money on the stock market. Urquhart recognised that he would face inevitable exposure should Rosanna die and Boyes claim his inheritance. However, Boyes was unaware of the will's contents and Urquhart reasoned that if Boyes were to die first, nobody could challenge him as sole remaining beneficiary, and his fraud would not be revealed.

After perusing A.E. Housman's A Shropshire Lad (in which the poet likens the reading of serious poetry to King Mithridates' self-immunization against poisons) Wimsey suddenly understands what had happened: Urquhart had administered the arsenic in an omelette which Boyes himself had cooked. Although Boyes and Urquhart had shared the dish, the latter had been unaffected as he had carefully built up his own immunity beforehand by taking small doses of the poison over a long period. Wimsey tricks Urquhart into an admission before witnesses.

Lord Peter Wimsey - Strong Poison