But following the inferno, police have found that the insulation did not pass any safety tests.
Temporary housing has been made available for the block's residents, who will only be allowed to return home after the potentially unsafe cladding is removed.
With millions of people working in thousands of office buildings up and down the country, the TUC says it is vital safety checks be carried out.
"Millions of people across the United Kingdom work in high-rise buildings, many of which could have cladding and insulation similar to that used in Grenfell Tower", said Frances O'Grady, TUC general secretary.
Speaking after the latest co-ordination meeting Mr Murphy said: "While preliminary work shows that there are no situations in Ireland directly comparable to Grenfell Tower, we must learn the lessons and take appropriate and balanced action to continue to minimise the probability of a large-scale fire tragedy occurring in Ireland".
A landlord in Manchester, northwest England, said Tuesday that safety tests had failed on 16 of its tower blocks, all clad with a similar aluminium composite material to that used on the Grenfell, although the product was different.
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"Something has clearly gone wrong over a number of years and we need to find out what, why and how to make sure it doesn't happen again", May told the BBC.
The charred remains of Grenfell Tower dominate the skyline in Kensington, London.
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.
Brighton director Martin Perry said: "We are fully satisfied that the American Express Community Stadium is entirely safe and that the materials and building practices used during the construction of the stadium, and our training ground, are of the highest standards". At this time, the safety of people living in these buildings is our paramount concern.
It is believed that the material may have contributed to the rapid spread of the fire through the 24-storey building.
Arconic, the U.S. supplier of the cladding installed in a refurbishment completed only past year, announced Monday that it was stopping sales of the material for high-rise buildings.