LONDON — The authorities in Britain are scrambling to conduct safety tests on at least 600 high-rise buildings with exterior cladding, after the fire at Grenfell Tower last week in which at least 79 people died.

Exterior cladding is thought to have contributed to the rapid spread of the fire on June 14, which engulfed Grenfell Tower, a 24-story apartment block in West London, in about an hour.

Samples of cladding from residential buildings over 18 meters (about 60 feet) in height are being sent to a national laboratory to check whether they are combustible. Tests have already shown that at least three buildings are at risk.

The cladding panels used at Grenfell Tower were of an aluminum composite material. Critics of the material have warned for years that aluminum surface sheets can melt in a fire, after which a blaze could race through the flammable polyethylene insulation between the sheets.

Prime Minister Theresa May’s announcement about the testing — made at the start of a parliamentary discussion — left lawmakers visibly surprised.

“Shortly before I came to this chamber, I was informed that a number of tests have come back as combustible,” Mrs. May told lawmakers. “The relevant local authorities and local fire services have been informed, and as I speak, they are taking all possible steps to ensure buildings are safe, and to inform affected residents.”

After the debate, Mrs. May’s office told journalists that 600 buildings had panels “similar” to those used in Grenfell Tower. The office later amended that statement, saying that the number 600 referred to tall buildings with aluminum panels, and that not all of them would have potentially combustible materials.

Sajid Javid, the secretary for communities and local government, was expected to provide further details later on Thursday.

The fire has focused attention on a variety of safety issues at Grenfell Tower and elsewhere.

The building, completed in 1974, did not have sprinklers or a centralized alarm system, though that is not uncommon for a high rise of its age. Lawmakers have chastised the government for failing to encourage the retrofitting of older buildings with sprinklers, as was recommended in a report on a deadly fire in Southeast London in 2009. A policy urging residents to “stay put” until rescue workers arrived has also been questioned.

Perhaps no issue has received as much attention, however, as the cladding, which was installed at Grenfell Tower as part of a renovation that was completed in May 2016.

Similar kinds of materials have been associated with fires in high-rise buildings in China, the United Arab Emirates and elsewhere.

The building contractor and cladding supplier involved in the Grenfell Tower renovation also worked on the refurbishment of another complex in London, Chalcots Estate.

The London borough of Camden, which owns that complex, announced on Thursday that the aluminum cladding panels “were not to the standard that we had commissioned.” It also said that it was considering legal action.

Officials emphasized that Chalcots Estate had “fire-resistant rock wool insulation designed to prevent the spread of fire, and fire-resistant sealant between floors, designed to stop a high-intensity flat fire from spreading to neighboring flats,” adding that those measures had helped contain a fire in 2012. Nonetheless, the borough said it would “immediately begin preparing to remove” cladding panels from five buildings in the complex.

Mrs. May urged building owners to have their structures tested immediately. “We can test over 100 buildings a day, and the results come within hours,” she said. “I urge any landlord who owns a building of this kind to send samples for testing as soon as possible. Any results will be communicated immediately to local authorities and local fire services.”

Mrs. May emphasized that landlords had “a legal obligation to provide safe buildings,” and said that owners would be asked to provide alternative accommodation if they could not fulfill this duty. “We cannot and will not ask people to live in unsafe homes,” she said.

Notably, Mrs. May did not repeat an assertion by two of her ministers, including Philip Hammond, chancellor of the Exchequer, that the kind of cladding used on the tower was illegal under British regulations.

If true, that would deflect responsibility for the disaster away from the government and toward the tower’s owners and building contractors, but a close examination of the regulations does not support the ministers’ assertions.

On Sunday, Mrs. May’s government took control of the emergency response, sidelining officials from the local council, the Royal Borough of Kensington and Chelsea, which owns the building. On Wednesday, the government said it would acquire 68 units in a luxury complex to permanently house displaced families.

The council’s chief executive, Nicholas Holgate, announced his resignation on Thursday, saying he had been asked to leave by Mr. Javid. The council had been heavily criticized as being slow to provide emergency aid to the survivors.

Mrs. May said she would appoint within days a judge to lead an independent public inquiry into the fire. The Metropolitan Police has opened a criminal investigation.

Grenfell Tower contained about 120 apartments, but Mrs. May said on Thursday that 151 homes had been destroyed, because the fire had spread beyond the tower.

On Thursday, 10 people injured in the fire remained hospitalized, five of them in critical condition.

Mrs. May’s statements did not mollify her critics, including Jeremy Corbyn, the leader of the opposition Labour Party.

Mr. Corbyn said that the residents’ longstanding concerns about fire safety had been ignored, and he suggested that had been part of a pattern of working-class people not being taken seriously.

He said that local councils had reduced fire inspections because of budget cuts, and that combustible cladding needed to be removed from all buildings, whatever the cost.

Mrs. May, who seemed poised and knowledgeable as she took numerous questions, did not say what would happen to residents of towers where combustible cladding was used, except that the government was “immediately acting to ensure the safety of people within.”