Around 800 people gathered outside Prime Minister Theresa May's residence at Downing Street to protest against the United Kingdom government's handling of the disaster, said Joey Ayoub, a journalist and activist who joined others at Number 10.
The current death toll from the tragedy reached 30 on Friday, with dozens more missing feared dead.
Six bodies have been recovered from the gutted 24-storey tower, while 11 have been located inside, but can not yet be removed.
The Queen speaks to firefighters who tackled the deadly blaze.
He described criticism of her response to the disaster as "terribly unfair".
Queen Elizabeth and her grandson Prince William visited a community centre Friday where some survivors are being housed, with volunteers inundated with donations of clothes and food.
She also pledged 5 million pounds ($6.39 million) of support, housing guarantees and help with access to bank accounts and cash.
Mrs May arrived in Downing Street on Saturday where she is chairing the Government task force on the disaster. But it is a awful tragedy.
One of the first victims was named as 23-year-old Syrian refugee Mohammed Alhajali, with the Syria Solidarity Campaign director Kareen El Beyrouty launching a campaign towards funeral costs.
Friday's visit represents May's second faux-pas in the aftermath of the fire.
The queen marked her official birthday Saturday by saying Britain remains "resolute in the face of adversity" after the horrendous fire and recent extremist attacks in London and Manchester. "We entirely support the calling of the public inquiry and will cooperate in whatever way we can with it so that local people have all the answers about what has happened", the council, the Royal Borough of Kensington and Chelsea, said.
The head of state said a saddened country was showing a determination to rebuild lives wrecked by "terrible" tragedy.
"I have friends in the tower and they are not telling us anything", said Salwa Buamani, 25, who came with her three-year-old niece on her shoulders.
"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected".
Saturday's newspapers conveyed the sense of anger on the streets.
Theresa May has met with residents of Grenfell Tower at her home in Downing Street just days after a devastating fire ripped through the building. Posters of missing people are pasted on many walls, and being worn as T-shirts.
Fire crews were again using water to damp down the high-rise building as they began a third day of picking through the debris. The protesters eventually made their way to busy Oxford Circus, where they staged a sit-in.
The search of the 24-floor building had been paused on Friday due to safety concerns, but has now resumed, Cundy said.
"People are terrified that the same thing could happen to them", said Khan.
Scotland Yard is leading the criminal investigation into the fire at Grenfell Tower to establish the exact cause of the fire. They examined the apartment where the fire started and determined "there is nothing to suggest the fire was started deliberately". A team of senior detectives is investigating. No sprinkler system was installed. The BBC said the London Fire Brigade has requested that service on two transit lines near the site of the fire be halted over concerns about the stability of the building.
Another man, who did not give his name, told police: "It's not your fault, she shouldn't have come".
"I had no idea how many people had got out by that stage, how many were trapped".
He added: "Particularly I can remember a kid's voice that was at a higher pitch screaming for help".