Combustible cladding has been found on seven high-rise blocks of flats in four local authority areas in England, Downing Street has said.
Samples taken from the buildings failed UK government tests to determine whether the cladding is combustible but that does not mean the tower blocks are unsafe, with that to be determined after more checks by the fire and rescue services, Theresa May's deputy spokeswoman said.
Landlords are informing tenants in the buildings about the failed tests and the next steps.
The spokeswoman told a regular Westminster briefing: "Failing this test does not necessarily mean that your building may be declared unsafe.
"It will be subject to further testing that is undertaken by the fire services to do that and if that is the case then we will be obviously working with local authorities and the landlords to make sure that nobody stays in a building that's proved to be unsafe."
Among the buildings so far confirmed by the British government to have flammable facades are the Chalcots Estate in north London, which is removing the cladding, and the Mount Wise Tower in Plymouth.
Both buildings were said to be enforcing more stringent fire-prevention measures as a response, including 24/7 observations of the building by safety teams.
Camden Council said the Chalcots Estate was facing renovation after tests found "the panels that were fitted were not to the standard that we had commissioned".
Plymouth Community Homes said of the at-risk high-rise: "It has been found to be aluminium coated with a polyethylene core, which has been rated as category 3 under the new controlled test conditions.
"The fire rating scale goes from 0 to 3 (with 0 being the highest safety score and 3 being the lowest)."
Elsewhere in north London, the residents of Rivers Apartments in Tottenham were greeted by a notice reading: "We want to let you know that we are carrying out an immediate review of the exterior cladding at Rivers Apartments, including an assessment by an independent fire safety expert."
Councils in England estimate that around 600 high-rise buildings have some form of cladding, with landlords asked to check if they used similar aluminium composite material (ACM) panels to Grenfell Tower.
It is suspected the material used to clad the exterior of the west London block accelerated the spread of last week's blaze, which has killed at least 79 people.
Labour leader Jeremy Corbyn called on the British government to ensure funds were available to make the high-rise structures safe.
He told the Commons this would be so councils "carry out immediate fire safety checks and install sprinklers" and said residents should be made aware of the timetable.
"There is obviously a huge cost involved in removing and recladding blocks that are found to have flammable materials included in them," he said.
"That resources, that money, must be made available immediately because it is a huge job of work, and when the Prime Minister says that those people who are in danger must be moved out of their properties - this is a massive undertaking and a huge focus of Government resources will have to go into it."
Responses from Scottish local authorities and the Northern Ireland Housing Executive suggest the type of cladding used in Grenfell Tower has not been used on their high-rise blocks
The company in charge of fitting the cladding to the affected Camden towers oversaw the refurbishment of Grenfell Tower, according to its website.
Rydon carried out the refit of the high-rises between May 2006 and October 2009.
Other samples are currently being tested by the Government, which has the facility to test 100 a day.
Communities Secretary Sajid Javid will shortly convene a subcommittee of the British Government's Grenfell Tower taskforce to look at building safety, after which he will provide an update.
He will also write to MPs on Thursday evening to set out what has happened so far and the next steps the Government is taking.