Prime Minister Theresa May has said there must be a "major national investigation" into the use of potentially flammable cladding on high-rise towers across the country over a period of decades.
Mrs May's call came as Cabinet was informed 95 samples of cladding from tower blocks in 32 English local authority areas have failed fire safety tests - amounting to 100% of all samples submitted by councils in the wake of the Grenfell Tower tragedy.
The PM's official spokesman said the national investigation could be conducted as a second phase of the public inquiry already announced into the west London blaze, which claimed the lives of at least 79 people earlier this month.
The latest tally of fire safety checks was presented to Cabinet by Communities and Local Government Secretary Sajid Javid, who has issued an urgent call for all councils to send in samples of cladding from tall buildings.
He has also said schools and hospitals may do the same where they have concerns.
Mrs May told the weekly Cabinet meeting there would have to be a "major national investigation" into what had gone wrong when cladding which is failing tests was fitted on buildings across the country over a number of decades, the PM's spokesman told reporters.
The exact nature of the investigation has not yet been determined, but one option is for it to form a second phase to the judge-led inquiry into the Grenfell fire, he said.
Evidence suggests the use of the suspect cladding stretches back at least into the last decade, the spokesman said.
Characterising the Cabinet response to the mounting evidence of widespread problems, he said: "It is clear that everybody is concerned about this and everybody wants to establish what went wrong."
Newham in east London and Sefton in Merseyside are the two latest areas to be identified as having at-risk towers.
Newham has three towers which were found with flammable panels, including Ferrier Point.
In Sefton, two towers have been discovered, a spokeswoman for the Department for Communities and Local Government has said.
There remain 15 areas which have not been named in which 56 buildings have failed the fire safety tests, she added.
The number of fires in high-rise purpose-built flats fell by almost half in the years leading up to the Grenfell Tower disaster, new figures from the Home Office showed on Tuesday.
Fears have also been expressed that contractors might have been confused by cladding with a category zero rating - meaning it has high fire resistance but is still flammable - mistakenly thinking this meant it was non-combustible.
The latest figures emerged as a fire safety expert raised doubts over the combustibility tests being carried out on cladding samples by the Building Research Establishment.
David Metcalfe, head of the Centre for Window and Cladding Technology, a body which works with hundreds of contractors, architects and manufacturers, claimed samples were being tested "severely" in a way which may be inflating the scale of the crisis.
Regulations in force refer to insulation products and filler materials, but do not specifically state that cladding should be of limited combustibility, he said.
The exact nature of the Government-backed tests has not been made public, but Mr Javid confirmed samples were being ranked on a scale of one to three - with those in categories two and three considered a failure.
Mr Metcalfe told the Press Association: "All these products are failing, which I don't think is any great surprise. The bigger issue is that it is not entirely clear whether or not the products, in accordance with the regulations, have to be of limited combustibility in the first place."
He explained: "Timber isn't an insulation product, it's not a filler material, so there's nothing stopping you using timber on a high-rise building, but the Government now are saying that all cladding should be of limited combustibility - there is a massive inconsistency there."
The Government was applying a "strict" interpretation of rules contained in an "unclear" regulatory document, Mr Metcalfe went on.
"They are interpreting that document to say the cladding should have been of limited combustibility but it doesn't actually say that," he said. "They are testing it more severely than might have been done in the past because people didn't think it required that level of testing."
His analysis follows claims on Monday by Housing Minister Alok Sharma that building regulations were "very clear" that the type of cladding used at Grenfell Tower was "non-compliant" on buildings over 18 metres (59ft).
Many councils have responded to news that their buildings' cladding failed fire tests by saying the non-combustible material used in the insulation mitigates the risk of flames spreading.
Asked if this meant the tests were making the risk to public safety appear greater than it was, Mr Metcalfe said: "What they are doing is probably about right, but it doesn't necessarily reflect what is going to happen on a building.
"You are testing a material in isolation. What we need to consider is how it performs as a system - it's the cladding, it's the support system, it's the insulation, it's the cavity barriers, it's all of these things combined that determines what happens in a fire."
Hospitals and schools are being tested to make sure they are not encased in combustible cladding, and Mr Javid said 15 buildings "across the wider government estate" require further investigation.
Mr Javid admitted on Monday that multiple fire safety inspection failures had been discovered in tower blocks which were evacuated last week in Camden, north London, including hundreds of missing fire doors, inaccessible stairways and breaches of internal walls.
Meanwhile, a residents' group has written an open letter to Mrs May and Home Secretary Amber Rudd, demanding immediate funding for legal advice for bereaved families and survivors.
It added: "The investigation must leave no stone unturned. It must identify each and every individual and organisation who must bear responsibility and accountability for this tragedy and the mishandling of the aftermath."
The number of displaced households now in emergency accommodation following the fire has risen to 386, the Grenfell Response Team said.
It added in a statement that more than £1,680,000 has been handed out to those affected by the blaze.
A housing group in Manchester said the number of its towers with cladding which failed the fire safety test has soared by 11.
A total of 16 high-rise buildings owned by One Manchester have now been found to be encased with combustible material.
The group said that despite the spate of failings, its buildings used non-flammable insulation.
Group chief executive Dave Power said: "We continue to take immediate action and have hired a contractor to remove all of the cladding which is made of aluminium composite materials.
That work will start today.
"Twenty-four-hour security is now in operation in every tower block to provide a 'wakeful watch' to raise the alarm and manage the building evacuation in the event of a fire, which we hope will provide extra reassurance for our tenants."
On Tuesday afternoon, work started to remove the cladding from the Hanover tower block in Broomhall, Sheffield, after it failed the new tests.
Residents in the 125 properties in the building have been told it is safe to stay in their homes while the work is carried out but temporary accommodation will be provided for anyone who wants to leave.
A Sheffield City Council spokesman said: "We have taken the decision to remove the cladding from Hanover tower block in Broomhall, Sheffield.
"We are checking the metal cladding on our tower blocks and it has now been confirmed a single element of the cladding system at Hanover has failed new fire tests."
Councillor Jayne Dunn, cabinet member for neighbourhoods and community safety, said: "Twenty-four tower blocks have been refurbished over the last 30 years and we have consistently used products that are widely used in the UK and have complied with building regulations.
"Sheffield City Council has asked for this independent assessment of all its tower blocks so tenants and residents can feel reassured and safe in their homes.
"We will not rest until we can assure tenants that our blocks are safe. We have carried out our own assessment which has revealed that the cladding on Hanover needs to be removed and we will do this straight away.
"We believe it is safe for people to remain in their homes and South Yorkshire Fire and Rescue Service is supportive of our approach."
Last week, the council announced that it would be fitting sprinklers to all 24 of its tower blocks.