Combustible cladding has been found on at least three tower blocks across the UK, with samples expected to be checked from many more.
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.
But there was confusion in Whitehall after Downing Street said that the 600 buildings had "similar cladding" to Grenfell Tower.
The Department for Communities and Local Government insisted that the figure referred to high buildings with any form of cladding, not necessarily ACM.
A DCLG spokesman said: "The situation is that 600 buildings have cladding, it is not similar, it is all types of cladding. Of these 600, we want landlords to check if they have ACM cladding.
"Of those 600, some of those would have ACM; we want to test them to see if they have ACM."
The Government has the facility to test 100 samples a day, with results produced within hours.
Flammable panelling on the outside of Grenfell Tower is suspected to have aided the rapid spread of last week's blaze, trapping dozens of residents inside.
A Number 10 spokeswoman said: "So far, three samples have been found to be combustible."
She added: "We are in touch with all the local authorities to encourage them to urgently send us the samples and then we will carry out the checks that we need to see where we are with that."
In blocks where the cladding is found to be combustible, "we will do a further test to make sure the building is safe" and residents could be rehomed.
"Obviously nobody will be living in buildings that are unsafe; they will be rehoused if they need to be and landlords will be asked to provide alternative accommodation where that's possible," the spokeswoman said.
The Prime Minister announced that a probe into whether cladding in Grenfell Tower met fire safety regulations will be published in the next 48 hours.
Theresa May faced questions over whether the material had passed fire and building safety tests when the west London tower block was refurbished.
Calls were made for combustible materials to be banned in tower blocks during an urgent Commons statement on the deadly fire.
Mrs May said: "My understanding is the fire service and the Building Research Establishment (BRE) - and BRE were there on the scene very early to look at this issue - they have been identifying the cause of the fire and any contributory factors to the fire.
"They are testing the cladding on the building and they expect to make the results of this public, I think in the next 48 hours."
Under pressure to introduce incentives for landlords to be given incentives to retro-fit sprinklers, she warned that "in not all cases will it be the case that the retro-fitting of sprinklers is actually going to be the thing that makes the difference".
Camden Council confirmed that cladding used on its Chalcots Estate in north London was to be removed after tests raised concerns about its safety.
Council leader Georgia Gould said: "The new results from the laboratory show that the outer cladding panels themselves are made up of aluminium panels with a polyethylene core.
"Therefore, the panels that were fitted were not to the standard that we had commissioned. In light of this, we will be informing the contractor that we will be taking urgent legal advice.
"Whilst we are clear that our cladding design and insulation significantly differs to that at Grenfell Tower, the external cladding panels did not satisfy our independent laboratory testing or the high standards we set for contractors."
Scottish local authorities' responses suggest the type of cladding used in Grenfell Tower has not been used on their high-rise blocks.
This is consistent with current building standards regulations in Scotland.
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.
Camden council said it would be conducting "24/7 fire safety patrols on the estate's corridors to reassure residents and carry out enhanced fire safety checks".
Three towers in Barnet, north-east London, were found to have similar rain screen panels on their cladding, but a non-combustible insulation material.
The Granville Point, Harpenmead Point and Templemead Point blocks had all been reclad in 2012, Barnet Council said.
"In line with the Government's advice to councils, samples from the investigation will be submitted to DCLG," a spokesman said.
The Northern Ireland Housing Executive manages 32 high-rise tower blocks. It has recently reclad two properties and is in the process of undertaking similar work at two others. The NIHE said the cladding was not the same as that used at Grenfell Tower.
"Before the cladding work started to the first tower block in North Belfast, we had the system thoroughly tested by the Building Research Establishment for fire safety," said a spokesman.
"The system was tested to BR135 standard. The Housing Executive is not complacent about fire safety and we are closely monitoring the emerging lessons from the investigations into the Grenfell tragedy and will take any action that is required to address fire risks."
The process of determining what, if any, cladding has been used on any other high-rise buildings in Northern Ireland, owned either by housing associations or private developers, is continuing.