Tensions in the local community have grown since Wednesday's deadly blaze at the Grenfell Tower in north Kensington which provided social housing for some 600 people.
Mohammed Alhajali, a Syrian refugee, was the first person to have been confirmed dead.
A second victim named yesterday was Khadija Saye, a 24-year-old photographer who had exhibited at the Venice Biennale.
British Prime Minister Theresa May has ordered a full public inquiry into the high-rise apartment blaze that killed at least 17 people in London amid growing public anxiety about whether similar blazes could occur in other housing blocks around the country.
"From a personal perspective, I really hope it isn't", Metropolitan Police commander Stuart Cundy said responding to speculation reported in The Telegraph and other media outlets that the number of dead could exceed 100.
Crowds are continuing to gather and a speaker called on demonstrators to remain in place until the council leaders make a statement pledging an independent investigation and rehousing for all those affected.
"It is very hard to find the words to express how those families affected must be feeling, and it is our job to work tirelessly to provide them with the answers they so richly deserve".
Firefighters are working their way through the smouldering remains of the building's 24 floors, but the fire is out.
Teams were forced to leave the building on Thursday afternoon when the fire restarted, delaying further the efforts to reach upper floors, where some victims are thought to have been trapped. "The severity and the heat of the fire will mean that it will be an absolute miracle for anyone to be left alive".
The cause of the blaze is under investigation, but a tenants' group had complained for years about the risk of a fire.
One of the girls is said to be in a coma, with her sister reportedly seriously traumatized.
She promised residents would be rehoused within three weeks, and rejected accusations that the government failed to act on recommendations to tighten fire regulations after a fatal block fire in London in 2009.
The focus of criticism is on the cladding fitted to external walls of the 1974 tower as part of a £8.7 million ($11 million, 9.9 million euros) refit completed previous year.
Local residents also say they are angry their safety concerns had been ignored and that people had been told to stay in their flats in the event of a fire.
The group's blog post argued that only "a catastrophic event will expose the ineptitude and incompetence of our landlord. and bring an end to the unsafe living conditions and neglect of health and safety legislation that they inflict upon their tenants and leaseholders".
Forensic experts said the fire at Grenfell was so hot it could be compared to a cremation, which is going to make it hard to identify all the victims.
The fire brigade also had to bring in specialist urban search and rescue dogs, which are lighter than people and can cover a larger area more quickly, to help find anything around the building that may help confirm the identity of those still inside.
"[This aims] to give the victims the immediate support they need to care for themselves and for loved ones", Ms May said.
More than £480,000 had been raised online for the victims by early Thursday, while local community centres were inundated by donations of clothes and food.
Kensington and Chelsea council said dozens of households had been provided with emergency accommodation.