Four tower blocks in Camden, north London, are among 60 high-rise buildings where aluminium cladding has been found to have failed fire safety tests.
Britain's government says the list of high-rise apartment towers fitted with external cladding that failed fire safety tests has grown to 60.
Conservative Prime Minister Theresa May, who has been criticized for her slow response to the Grenfell tragedy, said Saturday that the government was supporting Camden officials to ensure residents have somewhere to stay while building work is done.
Despite orders to evacuate to keep people safe, 83 people still refuse to leave their homes, according to the BBC.
The manufacturer of the insulation used to clad Grenfell Tower said they would stop using the product on high-rise buildings.
She gave assurances "immediate action" would be taken by councils in areas were tower blocks failed safety tests.
Over 100 people were evacuated late on Friday from buildings in Camden.
On Friday night, thousands of people living in 650 apartments in North London were forced to evacuate from their buildings over safety fears.
Emerging into the streets on a hot night, residents clutched children, pets and small amounts of clothing and food to try to find a bed in a local hotel or with family or friends.
Local authorities face a potential bill running into many millions of pounds to fund remedial work and, where it is deemed necessary, pay for alternative accommodation for residents should they need to be evacuated.
"It was farcical communication", 21-year-old Daniel Tackaberry told Reuters outside a nearby sports centre where the local council had laid out air beds.
Landlords should get potentially flammable building materials tested as soon as possible, he added. But we should not be in the position where buildings have such cladding on them. "It is therefore very important for local authorities and housing associations to continue to submit such samples as a matter of urgency", the minister said.
Public safety concerns have been prompted by exterior cladding known as aluminum composite panels, which are believed to have rapidly spread the fire at Grenfell Tower on June 14, trapping residents in their homes before firefighters could save them.
"Working with fire service experts to assess risks, a number of councils have already introduced other fire safety measures in buildings, such as 24-hour a day warden patrols, when advice from the fire service is clear that this will mitigate against fire risks ahead of the removal of cladding".
Georgia Gould added: "We realise that this is hugely distressing for everyone affected and we will be doing all we can, alongside the London Fire Brigade and other authorities, to support our residents at this hard time".