Camden Council in north London, which announced the evacuation Friday night, was the first local government to take the dramatic step of emptying its buildings so safety upgrades could be made.
More than 3,000 people were asked to leave four tower blocks in Camden, north London, this weekend after a fire audit revealed suspect gas fittings and faulty fire doors.
The London Fire Brigade concluded that the towers of 800 flats were unsafe and evacuated residents could spend up to 4 weeks in hotels while the cladding is removed from the building.
"Anyone living in a high-rise building can be reassured that their council will act on any advice from the fire service to ensure their safety", a spokesman said.
Combustible cladding used to insulate the tower and improve its appearance has been blamed for the rapid spread of the blaze.
Police investigating the cause of the deadly 24-storey Grenfell Tower blaze have said that the fire started in a fridge but spread rapidly due to the use of external cladding on the building, trapping residents in their beds as they slept.
Mrs May said: "We are making sure that the authority has the ability to do what is necessary to ensure people have somewhere to stay and that the work is done so that those tower blocks will become safe for them to return to in future".
He said officials knocked on residents' doors on Friday night, two hours after he had heard about the evacuation on the news.
Many residents complained about a lack of information and confusion.
The Metropolitan Police also said cladding attached to the 24-story public housing project during a recent renovation failed safety tests conducted by investigators, and that they have seized documents from a number of organizations.
In a statement, Mr Corbyn, who is at Glastonbury Festival, said: "Tower blocks across the country have now failed fire safety tests in the wake of the Grenfell Tower disaster".
Ms Gould said the fire service "told us they could not guarantee our residents' safety in those blocks".
"My thoughts are with residents being evacuated in Camden while their homes are made safe tonight", she said. To encourage cooperation, prime minister Theresa May said the government won't penalise any fire survivors who were in the country illegally.
More than 80 people are still refusing to leave their homes on the Chalcots Estate nearly 24 hours after a mass evacuation of four of the estate's five tower blocks.
Roger Evans, 51, who said he found out that his building was being cleared after a friend saw it on the news and alerted him by text, told the Press Association: "As far as I am concerned, nothing in that building has changed in the last few days, weeks, months or years". Other residents were distraught that they were ordered to evacuate, but were told to leave their pets behind in buildings that could be risky.
Police said Friday that they were considering filing manslaughter charges in the Grenfell disaster and they were conducting a wide-ranging investigation that will look at everything that contributed to it. "We are looking at all health and safety and fire safety offenses, and we are reviewing every company at the moment involved in the building and refurbishment of Grenfell Tower".