An estimated 600 high-rise buildings in England have cladding similar to that used on a London tower block which caught fire, killing at least 79 people, officials say.
Flames spread rapidly up the 24-storey residential Grenfell Tower last week, trapping people inside, in what was Britain's worst blaze since World War II.
Exterior cladding added during a refurbishment may have played a part.
The disaster in the London borough of Kensington and Chelsea heaped pressure on Prime Minister Theresa May, already fighting for her political survival after her party lost its parliamentary majority is this month's snap election.
The Grenfell tragedy has acted as a focal point for anger at local authority funding cuts, with accusations of criminal negligence.
"The estimate provided to us by councils is that there are approximately 600 high-rise buildings with similar cladding," Ms May's spokeswoman told reporters on Thursday. The government had no estimates yet for Scotland, Wales or Northern Ireland, she said.
"In terms of the people who are living in those buildings, we will do a further test to make sure the buildings are safe - obviously nobody will be living in buildings that are unsafe."
The spokeswoman said people would be rehoused if necessary.
Earlier Ms May announced that cladding used on some buildings had been found to be combustible. Her spokeswoman said three had tested as combustible.
"[We] should of course be careful on speculating what caused this fire, but as a precaution the government has arranged to test cladding on all relevant tower blocks," Ms May told parliament.
She said local authorities and fire services were taking steps to make affected buildings safe and to inform residents.
Ms May has launched a public inquiry into the fire and police have announced a criminal investigation.
Leaders of the council in the London borough of Camden said it would remove external cladding panels from five tower blocks on a local estate after finding they were not to the standard it had commissioned.
The council said it was informing the contractor which installed the cladding, made up of aluminium panels with a polyethylene core, that it was taking urgent legal advice.
It said that until the panels have all been removed, there will be round-the-clock fire safety patrols on the estate.
"This has been a wake-up call for the whole country," said Jeremy Corbyn, leader of the opposition Labour Party.
"Residents of tower blocks all over the country are concerned, worried and frightened for their own safety. What we need is a step change in our attitude towards housing in this country."
After apologising for a slow state response to the fire, Ms May said it was right that Nicholas Holgate, chief executive of Kensington and Chelsea council, had resigned. He said he was forced out by the government.