Prime Minister Theresa May, under pressure for keeping a distance from angry residents on a visit to the charred remains of the 24-storey block last week, said today the response to the disaster was "not good enough".
Her government is trying to make up ground in reacting to a fire that trapped people in their beds in the early hours of Wednesday, with many unable to escape as the flames raced up the building, cutting off exit routes and forcing some to jump.
Both May and her ministers have said they will do all they can to help those left homeless after the blaze and make sure other high-rise buildings, usually home to poorer people, are checked and safe.
But with Jeremy Corbyn, leader of the opposition Labour Party, emboldened by a better-than-expected result in an early election that wiped out the Conservatives' majority, May's government has been forced to justify cuts at a time when complicated talks to leave the European Union are beginning.
"If something needs to be done to make buildings safe, it will be done," finance minister Philip Hammond told the BBC's Andrew Marr show.
"Let's get the technical advice properly evaluated by a public inquiry and then let's decide how to go forward."
May has announced a public inquiry into the fire which would be fast-tracked. But on the streets, there is anger over whether the block's renovation project purposefully did not include safety devices, such as sprinklers, or used banned flammable materials to clad the building and make it more attractive for neighbours in the upmarket Kensington and Chelsea region.
Corbyn, who unlike May was quick to meet local residents and was praised for showing empathy, led calls for the government to drop its cuts - demands that Hammond said he was listening to.
"In the wake of (the) Grenfell fire we have to recognise that something has gone badly, badly wrong in this country, that predominantly poor people die in a towering inferno because possibly in the long term (there had been a) lack of public investment," Corbyn told ITV's Peston on Sunday programme.
"Somehow or other it seems to be beyond the wit of the public services to deal with a crisis facing a relatively small number of people in a country of 65 million."