Mr Corbyn, during a visit to the scene in west London, said the "truth has got to come out and it will".
London police commander Stuart Cundy told reporters that the number was expected to rise and firefighters have said they did not expect to find any more survivors after rescuing 65 from the inferno. "Without knowledge of the specific materials used we can not say at this early stage if any of the conclusions above are relevant to this tragic incident, but the increasing use of combustible materials in construction needs to be addressed if further events are to be avoided".
"London's fire commissioner says it would be a miracle if anyone is still alive inside", Larry Miller reports for NPR from London.
"It appears that the external cladding has significantly contributed to the spread of fire", said Angus Law from the BRE Centre for Fire Safety Engineering at the University of Edinburgh.
"My thoughts are with the victims, their families and all of those who had their homes destroyed", she said. Now that the smoke has cleared, the public could only gape at the huge burned-out hulk in the working class, multi-ethnic neighborhood.
A schoolgirl looks at messages of support for those affected by the massive fire in Grenfell Tower in London.
Grenfell Tower underwent a £10m refurbishment previous year and new thermal cladding system installed as part of this has been pointed to as the cause of the spread of the fire.
"Prince Philip and I would like to pay tribute to the bravery of firefighters and other emergency services officers who put their own lives at risk to save others".
Newspaper reports cited the planning documents for that neighborhood regeneration as stating that the cladding was chosen, in part, as a low-priced way to improve Grenfell Tower's external appearance to new neighbors in the expensive homes being constructed nearby.
Prime Minister Theresa May visited the scene on Thursday morning after promising a "proper investigation" amid growing concerns about how the fire could have spread so rapidly. The cause of the fire is under investigation, and authorities have refused to speculate on what could have started the blaze.
Emergency services have confirmed 17 people died in the tragic fire with 78 injured, 18 of which are in critical condition.
More than 200 firefighters, backed up by 40 fire engines, fought for hours to try to control the blaze, London's deadliest for a generation.
Some even threw their children to safety, with one witness seeing a desperate resident drop their baby from "the ninth or 10th floor" into the arms of a member of the public below. "Also, the fire escape plan for the building told residents to stay in their apartments behind supposedly fire safe doors".
At one point Rania, a carer and charity volunteer, is heard shouting outside of her window to the ground below for help while also trying to comfort her children, aged three and five. "This is where you find out how good it is to be a Londoner".
The cause of the fire is not known at this stage, the LFB said.
Witnesses said the flames spread quickly up the building as most residents slept, and photographs later on Wednesday showed an nearly entirely blackened, smouldering shell.