Testing potentially flammable material from high-rise towers should be pursued "urgently" by councils, a minister said, amid fears many more buildings are at risk.
Every cladding sample tested so far has failed fire safety tests, amounting to 60 high-rise buildings in 25 local authorities across the country, the Government said.
Amid signs the problem could escalate further, Housing Minister Alok Sharma called for samples to be submitted for examination quickly.
He further pushed for councils and landlords to take steps towards making the buildings in their care safe, even if results had not come back yet.
"Certainly, some councils are acting very quickly. We want all of them to be acting urgently on this," he told the BBC Radio 4 Today programme.
"People should not wait for the checks to come back from these (tests).
"They should act now, get the fire service in, check the buildings that they think may be affected, put in place mitigation measures if required, or, as in the case of Camden, if they need to evacuate, that needs to happen."
Concerns over fire safety triggered the mass evacuation of a north London estate on Friday, forcing thousands of residents from their homes.
The occupants of 600 flats on the Chalcots Estate were being moved into temporary accommodation, with officials warning they may not be able to return for up to a month while remedial work is carried out.
Prime Minister Theresa May is expected to be updated on the scale of the crisis when she chairs a meeting of the Grenfell Tower Recover Taskforce on Monday, Downing Street sources said.
Questions mounted over whether the cladding was illegal, with Mr Sharma refusing to be drawn on the subject when asked repeatedly on ITV's Good Morning Britain.
Asked at least five times whether the cladding was illegal or banned, he told viewers "from what we've seen it would suggest that the material used was combustible".
The building regulations, he said, were "very clear" that that type of cladding was "non-compliant" on buildings over 18 metres.
Pressed on whether a builder putting up a tower block today would be allowed to use this type of cladding, Mr Sharma replied: "The building regulations are very clear. Any building above 18 metres, this would be non-compliant.
Presenter Susanna Reid asked: "When you say non-compliant, do you mean it's banned?"
He said: "It means that you are not allowed to do it."
Asked again whether this meant it was illegal, he said: "Well, you are not allowed to do it, it is non-compliant.
"The regulations are very clear on this point, and clearly the public inquiry has been set up to investigate precisely what happened and we will get to the bottom of this."
He later assured the BBC that the Government was "literally working around the clock" to test samples that were being sent in from across the country.
On Sunday the Department for Communities and Local Government (DCLG) said Doncaster, Norwich, Stockton-on-Tees and Sunderland had buildings that failed tests, while Manchester, Plymouth and Portsmouth had already been named.
Islington, Lambeth and Wandsworth joined Barnet, Brent, Camden and Hounslow on the growing list of London boroughs, while 11 other areas are yet to be named.
A social housing provider in Liverpool also announced it had decided to remove cladding from two of its high-rise blocks as a precaution, following Government tests.
One Vision Housing said results showed "certain elements of the cladding" on Cygnet House and Wren House in the Bootle area of the city, "whilst meeting building regulations does not meet the latest DCLG test criteria".
The Liberal Democrats called on the Government to immediately ban the use of flammable materials in high-rise buildings.
London Mayor Sadiq Khan backed the Labour-led council's decision to evacuate the four high-rise blocks on the Chalcots Estate, saying: "You can't play Russian roulette with people's safety."
The Grenfell disaster will be raised in the House of Commons on Monday afternoon during an adjournment debate requested by Labour MP Jim Fitzpatrick.
The families affected by the fire have so far received £1,450,000, the Grenfell Response Team said on Monday.
Shadow chancellor John McDonnell caused controversy on Sunday when he said the victims had been "murdered by political decisions".
The June 14 tragedy left 79 people dead or missing presumed dead and many injured.
Hundreds more have been displaced and the Government and Kensington and Chelsea Council have come under fierce criticism over their response.
NHS England said on Monday that one person remained in critical care at the Royal Free Hospital in north London.
A further three people are still receiving treatment at the city's Chelsea and Westminster Hospital and King's College Hospital.
Questions over why cladding which breached fire safety rules appears to have been installed on tower blocks across the country are expected to be included in the public inquiry into the Grenfell Tower blaze, Prime Minister Theresa May's official spokesman said.
"It is clearly a huge concern that this is the case," the spokesman told reporters. "What is apparent is that this is on buildings across the country in local authorities run by all sorts of different parties.
"The job for the public inquiry will be to find out how and why this happened. I would expect that to be part of the terms of reference."
The spokesman was unable to confirm a date for the announcement of a judge to head the Grenfell inquiry and the publication of the terms of reference.
"We are making good progress in the appointment of a judge, in co-operation with the Lord Chief Justice, and we hope to be able to make an announcement as soon as possible," he said.
The spokesman said the authorities had the capacity to test 100 samples of cladding material a day and were nowhere near reaching that number.
"We are testing this material as soon as it comes to us and we request that landlords get this material to us urgently," he said.
Tests can be completed in a matter of hours and councils are informed immediately of the results, with appropriate action taken to ensure buildings are made safe, he added.
So far, evacuations have been necessary only in the north London borough of Camden, where there were other factors affecting safety, but in most of the affected blocks residents have been able to remain in place.