Dozens of demonstrators stormed Kensington and Chelsea town hall on Friday afternoon holding placards and shouting “we want an inquest” and “we want justice”.
Several people appeared to clash with security guards inside the building before more than 20 police officers restored order.
Protest organiser Mustafa Mansour read out a list of requests submitted to Royal Chelsea and Kensington Borough, including a commitment for the “immediate rehousing of all the victims… within the borough”.
Hundreds of protesters also marched on Whitehall, with some chanting “May must go”, bringing parts of London to a standstill.
The crowd then began marching towards Kensington High Street.
“We need answers and we need answers now,” a man said through a megaphone. “This should not be happening in the United Kingdom, this should never happen.”
Prime Minister Theresa May was confronted by angry crowds as she returned to the site of the fire in west London after being criticised for not meeting victims in the wake of the tragedy.
Mrs May met a group of victims, residents, volunteers and community leaders at St Clement’s Church near the scene of the blaze, but she declined to speak to anyone outside the building.
She faced cries of “coward” and “shame on you” as she left under heavy police escort, and police broke up a scuffle among the crowd as her car drove off.
The PM had earlier visited Chelsea and Westminster Hospital to meet staff and patients who were caught up in the fire.
In an interview, Mrs May was questioned over whether there was a need for the Government to accept some responsibility for what had happened.
“Something terrible has happened,” she answered.
“This is an absolutely awful fire that took place. People have lost their lives, people have had their homes destroyed, they have fled for their lives with absolutely nothing.”
Asked if she had misread the public anger, she replied: “What I have done since this incident took place is, first of all, yesterday ensure that the public services had the support they need in order to be able to do the job they were doing in the immediate aftermath.”
Hundreds of mourners stood arm in arm at a vigil on Friday night outside the Latymer Christian Centre, which has become the hub of a relief effort, co-ordinating aid and providing support for those displaced.
Many wept as they joined in with renditions of Bob Marley’s Three Little Birds and Amazing Grace during a short service which ended with a two-minute silence.
Police say that at least 30 people are now confirmed dead, but Sky News understands the number of missing – feared dead – is around 70.
Metropolitan Police commander Stuart Cundy said the tower remained “in a very hazardous state” but there was “nothing to suggest at this time that the fire was started deliberately”.
Mr Cundy vowed police “will get to the answer of what has happened and why”, adding: “If criminal offences have been committed it is us who will investigate that.”
Mrs May has said survivors would be consulted on the terms of reference for the full public inquiry, so they can obtain the answers they are seeking.
Jeremy Corbyn has written to Mrs May calling for the terms of reference to be wide enough to allow “all the relevant facts” to emerge and “all necessary lessons are learned”.
The Labour leader said he was “very concerned” that the probe is not used to “delay any parallel actions which might be taken by interested parties”.
Downing Street has announced a £5m fund for emergency supplies, food and clothing for victims.
And the generosity of the nation as well as those further afield has resulted in more than £3m being raised to help people affected by the fire get back on their feet.
The London Evening Standard launched an appeal on a dedicated website dispossessedfund.org.uk, raising nearly £1.5m by Saturday morning.
An appeal on JustGiving launched by Kensington Aldridge Academy teacher Hayley Yearwood has generated over £1,206,880.
And another set up by Karolina Hanusova has raised more than £388,240.