Dexter, a succesful businessman, is apparently killed when his car plunges over a cliff. His life is insured for a large sum but the insurance company is unhappy with details of the case, especially the fact that no body was found. Roper, the senior investigator of the Australian Life Insurance Company, is sent to Brighton to gather information, assisted by Trevor Bayliss, the local insurance agent.

In Brighton, Roper wastes little time in both exploiting his expense account and investigating the death himself; Inspector Wright of the local police informs him that the constabulary cannot be involved in a private matter. Roper also learns that Bayliss sold the policies to both Dexter and his business partner Turner, and that each insured the other's life. He also learns that Bayliss carried a torch for Dexter's widow Janet and that Dexter suffered no health worries. The proximity of a railway station to the cliff tops where the car caught fire leads Roper to suspect that Dexter faked the crash and made his way to the station.

Roper returns to London in the belief that no claim will be made. At home he meets with his GP, who asks that Roper place his mortally ill wife in a hospital. Roper refuses, insisting that he promised his wife that she would remain at home and that by watching every penny he could just about afford a full time nurse.

Janet Dexter does submit a claim and so Roper makes another visit to Brighton. On the advice of his employer, Mr. Player, Roper makes an appointment with Turner's secretary in the hope that plying her with alcohol will make her indiscreet. After several champagne cocktails she reveals that Turner was suffering from gambling debts and wished to sell the firm, but Dexter refused.

Convinced that he has uncovered the truth, Roper asks Inspector Wright, as well as Bayliss and Turner, to meet him at the local ponds. He explains his theory that Dexter was murdered by someone he knew well, who flagged down the car and disposed of the body in the nearby pits before making for the railway station. Roper claims that both Turner and Bayliss had reason to commit the crime but the presence of a gun in Turner's car leaves the Inspector with no doubt as to the guilty party. Turner attempts to kill Wright, but the Inspector has previously emptied the chamber. Turner is arrested and Bayliss reminds Roper that he can make a claim for the umbrella that was damaged in the fracas.