Dozens of protesters mounted the front steps and entered Kensington town hall. Some attempted to force their way past security personnel to the upper floors where local officials have their offices.
Some held fliers or wore t-shirts with images of fire victims and the word "missing" over the pictures.
One man approached a TV camera, saying, "We want answers and justice." He said the people don't want to be violent but they are desperate for information.
The protests come as British police say they may never be able to identify all of those who perished in the tower disaster, as anger and frustration mounted in the London neighborhood stunned by the tragedy.
A criminal investigation has been launched into the circumstances surrounding the blaze. Police said the cause of the fire was unlikely to be arson, but a team of senior detectives is investigating whether other offenses were committed.
One London Member of Parliament has called for corporate manslaughter charges to be brought, after it was revealed that flammable material had been used to clad the building during a recent refurbishment. No sprinkler system was installed.
Police said on Friday that 30 people were confirmed to have died and around 70 are unaccounted for. Relatives and friends of the missing made increasingly desperate appeals for information, as it became increasingly clear that few are likely to have survived.
Queen Elizabeth II and the Duke of Cambridge visited the area to meet residents and community representatives on Friday.
Theresa May slammed
The government of Prime Minister Theresa May, already weakened after losing its parliamentary majority in elections last week, has been slammed for a faltering response.
The London Mayor, Sadiq Khan, demanded that the government publish a list of other tower blocks checked by investigators by the end of Friday. In a letter to May, he listed a litany of concerns raised by residents, including the lack of information about missing relatives, the chaotic response of the local council, and concerns about safety in other tower blocks.
"They feel the government and local council haven't done enough to help them in the aftermath of this horrific incident, or to provide answers to their increasingly urgent questions," he wrote in the letter.
May, who has announced a full public inquiry into the disaster, faced criticism for failing to meet residents when she made a low-key visit to the scene Thursday. After widespread condemnation for failing to face residents in person, she visited victims in hospital Friday.
Police said on Friday that they had identified the place where the fire originated, and disclosed that it was unlikely to have been started deliberately.
Metropolitan Police Commander Stuart Cundy said there was "a risk that sadly we may not be able to identify everybody". He said 24 people remain in hospital, 12 of whom are in critical care.