"We want justice!", "Shame on you!", and "Killers!", the protesters shouted as they scuffled with security guards in the lobby of the building.
Some later left the red-brick building near Kensington High Street, a luxury shopping district, but around 30 remained inside in a tense standoff with about 30 police officers and a dozen security guards.
Hundreds of people, including singer and human rights campaigner Lily Allen, were protesting outside the town hall of Kensington and Chelsea, holding up cardboard signs reading "Justice for Grenfell".
One protester held up a "Wanted" poster for the head of the Kensington and Chelsea Tenant Management Organisation, which administers Grenfell Tower, accusing him of "corporate manslaughter".
The tower is in a working-class enclave near the multimillion-pound homes of Kensington.
"It is criminal to wrap homes in flammable plastic," read another sign after it emerged that cladding installed on the exterior walls of the tower as part of refurbishment was officially graded as not fire-resistant.
Residents had long complained about fire safety risks at Grenfell Tower during a refurbishment project completed last year, but said their concerns went unheeded.
"We are in the richest borough in the UK and in this very borough we have a building where some of the poorest live and the safety measures are totally inadequate," said Mustafa Al Mansur, one of the organisers of the demonstration.
"We need to know what commitment the council is taking to ensure this tragedy is not repeated," he said. "We need to know exactly the number of people who were there during this tragedy."
Police have said 30 people are confirmed dead after the blaze, while media reports have said more than 70 are still unaccounted for.
Local residents have accused police of hiding the true toll.
There were chaotic scenes as angry protesters shouted through a loudspeaker.
"We are in pain. We have been trodden on by people who say they are there to protect us," one woman said.
Another said: "It was a death trap and they knew it."
The protesters also held up pictures of those still missing and now feared dead.
"No justice, no peace!" the crowd shouted.
"I have friends in the tower and they are not telling us anything,"Salwa Buamani, 25, told AFP.
"We are not given information about our loved ones," she added.
"We are not here to trouble people. We just want answers," said Buamani, who came to the protest with her three-year-old niece on her shoulders.
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