Prime Minister Theresa May today warned that the cladding of a number of tower blocks in Britain has been found to be “combustible”, as the first head in the aftermath of the Grenfell Tower blaze rolled with the local council’s chief executive resigning amid criticism.

Nicholas Holgate claimed he was forced to step down as head of the Kensington and Chelsea Council over the authority’s response to the fire tragedy that claimed at least 79 lives by the government’s Communities and Local Government department.

May, in a statement to the House of Commons this morning, said that the council “couldn’t cope” in the aftermath of the fire, and that it “was right” that the chief executive had stepped down. She also told Parliament that additional fire safety checks carried out on similar tall buildings and towers blocks in the city had revealed that the cladding used in some cases was made up of “combustible” material.

“As a precaution, the government has arranged to test cladding in all relevant tower blocks. Shortly before I came to the chamber, I was informed that a number of these tests have come back as combustible,” she said. “The relevant local authorities and local fire services have been informed, and, as I speak, they are taking all possible steps to ensure buildings are safe and to inform affected residents,” May said.

While the cause of the Grenfell Tower fire is yet to be confirmed, there is widespread speculation that it was the rain-screen cladding used on the outside of the building for insulation purposes that led to the fire spreading too rapidly.

The British premier told Parliament that as many as 151 homes had been destroyed in the massive fire on June 14, most of them in Grenfell Tower and some in the vicinity of the building. She said that all survivors will be rehoused in equivalent homes and that around 68 flats have already been offered at cost price in a new block of flats in the area. “For any guilty parties, there will be nowhere to hide,” she said, adding that the Grenfell Tower investigation will not be used as a pretext to carry out immigration checks.

“I would like to reassure people that we will not use this tragic incident as a reason to carry out immigration checks on those involved or on those providing information to identify victims or those assisting with the criminal investigation,” May said. “We will make sure that all victims, irrespective of their immigration status, will be able to access the services they need, including healthcare and accommodation,” she said.

Opposition Labour party leader Jeremy Corbyn also welcomed the resignation of the Kensington and Chelsea council chief executive but called for more action against the local council.

In his resignation statement, council chief Holgate said, “Serving the families so desperately affected by the heart-breaking tragedy at Grenfell Tower remains the highest priority of the council. If I stayed in post, my presence would be a distraction.”

“I strongly believe that councillors and officers have always endeavoured to have the interests of our residents at heart and will continue to do so,” he added. Holgate said the Communities and Local Government Secretary Sajid Javid had “required the leader of the council to seek my resignation”.

However, a spokesperson from the Department for Communities and Local Government denied involvement, saying, “The appointment of chief executives is entirely the responsibility of the local authority.”

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