LONDON >> British police today described the painstaking work of recovering remains from a burnt-out London high-rise, as they tried to reassure grieving families that everything possible is being done to identify and retrieve the dead.

Police say at least 80 people died in the June 14 fire at Grenfell Tower, but only 34 victims have formally been identified. Detectives say it will take months to identify all the victims, and the agonizing wait has provoked anger and dismay from victims’ families.

Four weeks after the blaze, some residents of the public housing tower question the official death toll, insisting the true number is higher than 80. Many also complain of agonizing delays in getting information and assistance and in finding new places to live.

Sgt. Alistair Hutchins, a member of the Metropolitan Police’s disaster victim identification unit, said officers are carrying out a methodical search of the 24-story tower block, working on their hands and knees with shovels and sieves to retrieve fragments of bone or teeth that can be used to identify victims.

Police and forensic anthropologists plan to sift through 15 metric tons (17 tons) of debris on each of the building’s floors. So far, police say they have made 87 “recoveries” of human remains — but they may not be from 87 different people.

Officers believe no one survived from 23 of the building’s 129 apartments.

In an interview released by police, Hutchins said he understood the frustration of victims’ families.

“All I can say is please be patient, we are doing our utmost best for you. And we are working as hard as we can,” he said.

Police, the British government and the local authority that owns Grenfell Tower have all faced accusations that they were slow to grasp the magnitude of the tragedy — the country’s deadliest fire in more than a century — and flat-footed in their responses.

The blaze ravaged a building that was home to many working-class residents in one of London’s wealthiest areas. The local authority, Kensington and Chelsea Council, is facing criticism over alleged cost-cutting during renovations that covered the tower in flammable aluminum cladding. The composition of the exterior panels helped fuel the fire’s rapid spread.

The fire has produced a crisis of faith in British government and public institutions.

Incoming Kensington council leader Elizabeth Campbell — selected after her predecessor resigned in the wake of the fire — acknowledged today it would take “a generation” to rebuild trust between Grenfell residents and the local government.

During a debate in the House of Commons today, lawmakers listed a litany of problems, from government spending cuts to regulations that don’t require sprinklers in all buildings.

Labour lawmaker Ellie Reeves said the disaster “is symptomatic of a system that is broken — a system that neglects the poor and vulnerable, a system where cost-effectiveness seems to have been put before health and safety.”