It came as inquests were opened and adjourned at Westminster Coroner’s Court into the deaths of five victims, with a married couple officially named as among the dead.
Omar Belkadi, 32, died from inhaling fire fumes, while his wife, Farah Hamdan, 31, was killed by smoke inhalation.
They lived on the 20th floor of Grenfell Tower with their daughters Malek, seven, Tazmin, six, and Leena, just six months old.
The two eldest daughters were found in hospital by family members but the fate of their youngest girl remains unknown.
Abufars Ibrahim, 39, died of multiple injuries, while Anthony Disson, 65, and a 52-year-old woman, Khadija Khalloufi, both died from inhalation of fire fumes.
A highly toxic gas released by insulation on the outside of the building is believed to have contributed to a number of deaths.
The boards, fitted during a refurbishment of the tower, could have produced enough deadly hydrogen cyanide to fill every flat, it has been reported.
Richard Hull, professor of chemistry and fire science at the University of Central Lancashire, told Sky News: “The outside wall of the building had 150mm of PIR foam (fitted), and once the fire had spread to that every flat would have its own source of PIR foam, which would have produced enough hydrogen cyanide to kill all the people in that flat.”
Manufacturer Celotex stated that the insulation would have released “toxic gases” if it caught fire.
King’s College Hospital confirmed to Sky News that three of its 12 Grenfell patients were treated with the hydrogen cyanide antidote Cyanokit.
Earlier on Wednesday a funeral for 23-year-old Syrian refugee Mohammad Alhajali, the first victim to be identified, was attended by his family and London mayor Sadiq Khan.
It was also announced that 68 flats around 1.5 miles from Grenfell tower in the borough of Kensington and Chelsea had been purchased by the City of London Corporation in a deal brokered by the Homes and Communities Agency (HCA).
An independent public advocate to help bereaved families after major disasters was announced in the Queen’s Speech the same day.
The speech confirmed plans for a public inquiry into the tragedy and a new strategy for resilience in major disasters could include a Civil Disaster Reaction Taskforce to help at times of emergency, and an independent advocate will support those affected and help them at inquests.
The Grenfell Tower Response Team said 249 households are in emergency accommodation in hotels and £675,000 has been handed out to families affected by the disaster.
Mrs May went on: “I know many others living in tall residential buildings will have concerns about their safety after what happened at Grenfell.
“All social landlords have been instructed to carry out additional fire safety checks on tower blocks and ensure the appropriate safety and response measures are in place.”
She added: “We’ve also taken steps to make private landlords aware and make our checking facilities available to them for free.
“The House should, of course, be careful on speculating what caused this fire.
“But, 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.
“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.”
The Prime Minister said that 79 people had been confirmed dead or listed as missing presumed dead and the death toll, which includes children and whole families, was likely to rise further.
Outlining the response to the tragedy, she said: “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.
“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.”
Mrs May told MPs that Kensington and Chelsea Council “could not cope” and said it was right for chief executive Nicholas Holgate to resign.
More than £700,000 has been paid out to victims so far, who will not have be expected to repay the cash, and a central command centre has been set up to control the response, with more than 600 people working to support victims in the area.
Labour leader Jeremy Corbyn said the residents of Grenfell Tower were “let down both in the immediate aftermath and so cruelly beforehand”.
He said the public inquiry “must establish the extent and by who”.
“At least 79 people are dead - it is both a tragedy and an outrage because every single one of those deaths could and should have been avoided,” he added.
Mr Corbyn asked Mrs May why the political leaders of Kensington and Chelsea Council were not “taking responsibility as well for this whole dreadful event”, following the resignation of the chief executive.
He said: “From Hillsborough, to the child sex abuse scandal, to Grenfell Tower - the pattern is consistent: working-class people’s voices are ignored, their concerns dismissed by those in power.
“The Grenfell Tower residents and North Kensington community deserve answers and thousands and thousands of people living in tower blocks around the country need very urgent reassurance.”
He added that firefighters were “traumatised”, “overstretched and understaffed” in the wake of the London Bridge terror attack and the Grenfell blaze, and called for the “whole issue of the security of our fire service” to be looked at.
Promising an interim report from the public inquiry “as soon as possible”, Mrs May said: “For too long residents have been overlooked and ignored.
“We will ensure that they are involved in every step of this process.
“No stone will be left unturned in this inquiry and for any guilty parties there will be nowhere to hide.”
She praised volunteers, businesses and public servants for “stepping up” to help in the time of crisis, paying tribute to people of Kensington to opening their homes to victims.
Mrs May acknowledged that many people were “mistrustful” of the Government as she promised that ministers would never forget the victims of the tragedy.
She said: “As we move forwards, so we must also recognise that for too long in our country under governments of both colours, we simply haven’t given enough attention to social housing.
“And this itself is actually a symptom of an even more fundamental issue. It shouldn’t take a disaster of this kind for us to remember that there are people in Britain today living lives that are so far removed from those that many here in Westminster enjoy.”