Jeremy Corbyn has described the Grenfell Tower fire as an "outrage", adding: "Every single one of those deaths could and should have been avoided."
The Labour leader was speaking after Theresa May gave MPs an update on the tragedy and revealed that tests on cladding on other tower blocks had found it to be combustible.
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.
The Prime Minister 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."
But responding to her statement, Mr 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".
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."
Referring to warnings about safety from Grenfell residents before the tragedy, he added: "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 said 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 examined.
The Commons statement came hours after 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.
Campaigners welcomed the departure as overdue but urged Mr Javid to ratchet up pressure on the Conservative leader of the council, Nicholas Paget-Brown.
In the Commons, Mr Corbyn questioned why the political leaders of the council were not "taking responsibility" as well as the chief executive.
The Commons statement came as:
:: It emerged that as well as being combustible, the insulation in the 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.
Mrs May told the Commons she expected the judge leading the public inquiry to bring out an interim report, and said: "I would expect within the next few days to be able to announce the name of the judge.
"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."