LONDON — It was a case that riveted the world: In 1974, a dashing British aristocrat and army officer, known for his prowess at backgammon and bridge and his fondness for vodka martinis, powerboats and Aston Martin cars, vanished after the bludgeoned body of his children’s nanny was found in the basement of his family’s house in the affluent Belgravia area of London.

The aristocrat, Richard John Bingham, the seventh Earl of Lucan, was declared the killer in 1975. But he was never found, despite an international manhunt; unverified sightings in places as far-flung as Australia, Colombia, India, Paraguay, the United States and New Zealand; and endless conspiracy theories. In the United States, the case has been compared to that of Joseph Force Crater, a New York judge and bon vivant whose 1930 disappearance was never solved.

A British judge declared Lord Lucan dead in 1999, allowing the resolution of certain estate and inheritance matters, but that ruling did not definitively close the issue. Under a law that took effect in 2014, the earl’s son, George Charles Bingham, asked a court to formally issue a death certificate so that he could inherit his father’s title and become the eighth Earl of Lucan.

A High Court justice, Sarah Asplin, granted Mr. Bingham’s request in London on Wednesday. The proceeding, which attracted significant attention in the British media, was surprisingly brief for a case with such a notorious and lengthy history.