The Prime Minister will be updated on the Grenfell Tower recovery effort later as the number of high rises feared to pose similar fire risks mounts.
Cladding samples from 60 high-rise buildings in 25 local authorities across the country have failed fire safety tests ordered after the tragedy.
Of the first 34 samples tested from 17 local authorities, there was a 100% failure rate, Communities Secretary Sajid Javid said on Saturday.
Theresa May is due to chair a meeting of the Grenfell Tower Recovery Taskforce on Monday, Downing Street sources said, and is likely to hear how many of the country's high rises are swathed in potentially flammable material.
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.
Camden Council said concerns over cladding on the buildings had led to further fire safety issues being identified in the blocks and the evacuation was ordered following consultation with fire officers.
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.
On Sunday a social housing provider in Liverpool 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.
Meanwhile, 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."
Shadow chancellor John McDonnell caused controversy on Sunday when he said the victims of the Grenfell disaster in west London 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.
Speaking at the Glastonbury music festival, Mr McDonnell said: "Is democracy working? It didn't work if you were a family living on the 20th floor of Grenfell Tower.
"Those families, those individuals - 79 so far and there will be more - were murdered by political decisions that were taken over recent decades.
"The decision not to build homes and to view housing as only for financial speculation rather than for meeting a basic human need made by politicians over decades murdered those families."
The Grenfell disaster will be raised in the House of Commons on Monday afternoon during an adjournment debate requested by Labour MP Jim Fitzpatrick.