LONDON — A British government inquiry into the deadly inferno at a London high-rise for working-class tenants will examine the conduct of the local authorities, but not the broader issues involving low-income housing, the government said on Tuesday.

The June 14 fire at the high-rise, the Grenfell Tower, a neglected 24-story complex in one of London’s most affluent boroughs, left at least 80 people dead and laid bare the class divisions in the heart of the British capital.

Martin Moore-Bick, a retired judge who will be leading the investigation, said in a letter to Prime Minister Theresa May made public on Tuesday that he had established the terms of the inquiry after meeting with victims, family members and other interested parties.

The letter said that the inquiry would examine the arrangements made by the local council of the Royal Borough of Kensington and Chelsea, in particular the way in which it received and acted upon information related to the risk of fire at Grenfell Tower, “and the action taken in response to such information.”