Jeremy Corbyn has said each of the Grenfell Tower fire deaths "could and should have been avoided", as it emerged combustible cladding has been found on at least 11 other tower blocks.
Mr Corbyn compared the tragedy with the Hillsborough disaster and child abuse scandals, saying: "The pattern is consistent: working-class people's voices are ignored, their concerns dismissed by those in power."
And he said thousands of people living in tower blocks around the country needed urgent assurances about their own safety.
Downing Street has since confirmed that 11 blocks of flats in eight local authority areas in England have been found to have flammable facades, with tests being conducted urgently to see if many more could have the same material, which is suspected of helping the Grenfell blaze spread.
Updating MPs on the tragedy earlier on Thursday, Prime Minister Theresa May 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."
Mrs May also said the tragedy will not be used to carry out immigration checks on those affected or on those providing "vital" information to identify victims or to assist the criminal investigation into the fire.
She said "no stone will be left unturned" in the inquiry into the tragedy, adding: "For any guilty parties there will be nowhere to hide."
Mrs May told the Commons she expected the judge leading the public inquiry to bring out an interim report, and said: "What I think we very much want to ensure is that when the judge takes charge of this inquiry that people feel, as I said earlier, that they can have full confidence in the inquiry and so we are taking steps to ensure that that's the case."
In reply, Mr Corbyn said the residents of Grenfell Tower were "let down both in the immediate aftermath and so cruelly beforehand" and that the public inquiry "must establish the extent and by who".
Mr Corbyn told MPs: "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."
Two of the 11 buildings so far confirmed by the Government to have flammable facades are the Chalcots Estate in north London, which is removing the cladding, and the Mount Wise Tower in Plymouth.
A third building is in the Manchester area.
But while the samples taken from the 11 buildings failed Government tests it did not mean the tower blocks were unsafe, with that to be determined after more checks by the fire and rescue services, Mrs May's deputy spokeswoman said.
Separately, Newlon Housing Trust confirmed the 22-storey tower block Rivers Apartments, in Tottenham, north London, was clad with Reynobond PE - which Grenfell tower was reportedly covered with.
A spokesman said the London Fire Brigade had carried out a safety audit and were satisfied it was a "low-risk fire building", adding that they would comply with any further instructions.
The housing association was awaiting recommendations from experts to determine whether the cladding should be replaced, he added.
Grenfell Response Team said almost £1 million had been distributed to affected families as of Thursday afternoon, with 354 households within the cordon area placed into emergency accommodation.
Some 140 hotel placements have been made for people living in Grenfell Tower and Grenfell Walk while there are 109 households now in hotels from the wider affected area.
There remain 21 households from Grenfell Tower and Grenfell Walk who have been contacted but have not had their housing needs assessed yet.
Earlier on Thursday, Kensington and Chelsea council's chief executive Nicholas Holgate was forced to quit by Communities Secretary Sajid Javid after the local authority's handling of the crisis came under intense criticism.
London Mayor Sadiq Khan called for more heads to roll, while campaigners urged Mr Javid to ratchet up pressure on the Conservative leader of the council, Nicholas Paget-Brown.
Mr Khan said the entire leadership of Kensington and Chelsea council should be considering their positions and that there was "not a chance in hell" that residents "will have the semblance of confidence in that council until they see a change in leadership".
In the Commons, Mr Corbyn questioned why the political leaders of the council were not "taking responsibility" as well as the chief executive.
Mr Paget-Brown later issued a statement apologising for a "failing in our collective response" to the fire, admitting co-ordination on the ground could have been better and re-homing people was not "as fast as we would have liked".
In other key developments:
:: It emerged that as well as being combustible, the insulation in the Grenfell cladding released highly toxic gas and some victims were treated with the hydrogen cyanide antidote Cyanokit.
:: The renovation work carried out on the tower before the fire was inspected 16 times by the council.
:: NHS England said that 10 patients were still receiving care across four London hospitals. Five of these are in critical care.
:: The Government announced that victims have had their outstanding energy bills written off by power companies.
:: Residents living in high-rise buildings spoke of their fears after learning their homes are covered in combustible cladding
:: Leader of Birmingham city council John Clancy said all 213 blocks in the authority's area would be fitted with a sprinkler system regardless of whether the Government will pay.
Liberal Democrat peer Lord Newby accused the PM of hypocrisy in her statement, in which she said the fire had underlined the plight of poorer families and pledged to "stand up for them".
Lord Newby argued the Conservatives had fought the election on a platform of cuts to school funding, benefits and local government.
He said: "This hypocrisy makes me very, very angry."
He called on the Lords leader to suggest to Mrs May "that if she really does wish to stand up for people like the tenants of Grenfell Tower she starts to adopt policies that actually follow her words".
The Archbishop of Canterbury sought assurances from the Government that there would be "no budgetary constraints" on providing support for those emergency workers who risked their lives in facing the "absolute horror" of dealing with the fire and recent terrorist atrocities.
The Most Rev Justin Welby called for those welfare services to be "adequately funded above and beyond their normal provision".
He also said in the aftermath of the fire, faith communities had worked together in a way "that put a complete lie to the divisions that had sought to be created by the terrorist attacks", adding that it was "the most powerful visual image" of "unity around suffering".