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.
Aluminum composite panels used as exterior cladding are believed to have rapidly spread the fire in London on June 14, trapping residents in their homes before firefighters could save them.
Meanwhile, Sky News has uncovered research that questions the European safety certification of widely used insulation panels containing the same PIR plastic used behind the cladding at Grenfell Tower.
Paulous, who lived with his family on the apartment tower's 18th floor, perished as his family tried to escape the blaze.
Police secures a high-rise residential building from which the city of Wuppertal evacuated around 80 people after it was found to contain flammable materials, in Wuppertal, Germany, June 27, 2017.
Theresa May's spokesman said it would examine what had gone wrong 'when cladding which is failing the tests was fitted on buildings across the country over a number of decades'.
Britain's prime minister on Tuesday ordered an investigation into cladding and insulation on high-rise towers across the country, as authorities struggled to contain the risk from construction materials that leave tall structures vulnerable to catastrophic fires. Sajid Javid, Secretary of Sate for Communities and Local Government, announced on Monday that, so far, every sample received as part of the testing program had failed to meet fire safety standards.
Local residents have said the total strikes them as suspiciously low - a concern echoed on Monday night by Labour MP David Lammy, who suggested information could have been held back to prevent a riot.
"Following the incident at Grenfell Tower, the county council has instigated a further review of its assets".
Nine hospital trusts have been identified as using cladding that is similar to that involved in the Grenfell Tower fire. "I know that the will to positively contribute from professional bodies and others is strong and we will deploy this to support our work".
One of them, Mr Fleming, said the incident at Grenfell in London is a "game changer" for the fire service. "However, we are talking to the trusts and will work with them to reassure patients and visitors as required".