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Community centres were inundated with donations from across London and the UK
Prime Minister Theresa May has ordered a full public inquiry into the fire that engulfed a west London block of flats, killing at least 17 people.
That figure is expected to rise, as fire chiefs do not expect to find any more survivors in the burnt-out Grenfell Tower, in north Kensington.
People have been desperately seeking news of missing family and friends.
The PM said people “deserve answers” as to why the fire spread so rapidly and that the inquiry “will give them”.
Mrs May, who made a brief, private visit to the scene earlier, said: “[The emergency services] told me that the way this fire had spread and took hold of the building was rapid, it was ferocious, it was unexpected.
“So it is right that, in addition to the immediate fire report that will be produced and any potential police investigation, that we do have a full public inquiry to get to the bottom of this.”
Labour leader Jeremy Corbyn, also visited the site, telling community leaders “the truth has to come out”.
Number 10 confirmed the inquiry will be judge-led.
The BBC’s assistant political editor Norman Smith: “It (the inquiry) will almost certainly hold its evidence sessions in public and those who will give evidence will include the local council, the builders, the contractors but yes too, I suspect the tenants and the relatives of some of the victims,” he added.
Housing minister Alok Sharma said the government is working with the local authority to ensure that “every single family will be re-housed in the local area”.
Fire minister Nick Hurd called the fire a “national tragedy” and said there was “no room for plodding bureaucracy”.
He said there should be “no stone unturned on this because we completely understand the shock, the concern, the anger, the frustration, the fear that is out there”.
Firefighters were called to the 24-storey residential tower in the early hours of Wednesday, at a time when hundreds of people were inside, most of them sleeping.
Many were woken by neighbours, or shouts from below, and fled the building.
Fire crews rescued 65 adults and children, but some stayed in their homes, trapped by smoke and flames.
More than 30 people remain in hospital – 17 of whom are in a critical condition.
The Queen earlier said her “thoughts and prayers” are with families.
By Lucy Manning, special correspondent, BBC News
For the families of the missing, grief is mixing with anger.
They are angry at the lack of information about their relatives. Many just don’t know if they are alive, dead or injured.
I spoke to one man: His cousin, her husband and their baby are missing.
He is pleading for the police, the hospitals, the authorities to give him information about those who are injured or who might have died.
It’s a complaint I’ve heard from families after terror attacks: that the system doesn’t seem to help the families. That the wait is too long and agonising.
His relatives had to trawl round hospitals and, thanks to a nurse, found two missing children but they haven’t found the rest of the family.
Although it’s hard for the authorities to deal with these incidents his message to the police, hospitals, officials and politicians is “please please help us.”
On Thursday morning, London Fire Commissioner Dany Cotton said her crews had identified a “number” of those killed, “but we know there will be more”.
Asked how many were still missing, Met Police Commander Stuart Cundy said it would be “wrong and incredibly distressing” to give a number.
“I know one person was reported 46 times to the casualty bureau,” he said.
A brief search of all floors in the tower had been carried out, but the severity of the fire and amount of debris meant a thorough search would be “difficult and painstaking”, Commander Cotton said.
BBC