The death toll after the latest update could be around 70 people.
The horrific fire early Wednesday morning has put increased pressure on Prime Minister Theresa May and her senior ministers at a time when her authority has been weakened by an election that saw her Conservative Party lost its majority in Parliament.
CTMO, the Kensington and Chelsea Management Organization, has managed the building on behalf of local public authorities who own it. Many questions also center on the speed at which the fire spread.
Police said Saturday that 30 people had been confirmed dead since the fire, while another 28 remain missing and are presumed dead.
The Sunday Mail says a multi-million-pound tower cladding project was nearly scrapped amid fire safety fears - before the Scottish government "changed the rules and deemed it safe".
The area surrounding the tower has been plastered by distraught relatives with pictures of the missing, from grandparents to young children.
Morocco said seven of its nationals were among the dead.
He is hopeful the two-and-a-half hour meeting, attended by victims, residents, community leaders and volunteers, was the starting point for a process of "lasting change".
The specific cladding used in the Grenfell Tower renovation has been identified as a cheaper and more flammable variety, amid confusion over whether the material is legal in the UK.
"We have colleagues in there as we speak, searching for and recovering those that have died".
A man from the delegation, who did not give his name, told reporters they would make a full statement "in the community".
"I have friends in the tower and they are not telling us anything", said Salwa Buamani, 25, who took part in the peaceful protest outside with her three-year-old niece.
The No 10 meeting came after Mrs May chaired an emergency session of the Grenfell Recovery Task Force.
Every household whose home has been destroyed as a result of the fire will receive a guaranteed £5,500 minimum down payment from the fund, the government has said.
After having spoken to many members of the congregation as well as others who came in after the service to see him, Mr Khan paid tribute to the local community for its resilience but said a feeling of anger remains.
May was criticised for avoiding locals when she visited the charred shell of the 24-storey building on Thursday and faced cries of "Shame on you" and "Coward" when she returned on Friday.
"Newspapers are calling May's decision not to meet survivors the day after the blaze her "Hurricane Katrina" moment", NPR's Frank Langfitt notes.
"The country has witnessed a succession of bad tragedies".
She stood for a minute's silence before her 91st birthday parade on Saturday.
Councilor Nicholas Paget-Brown told the BBC this week that sprinklers were not fitted inside the building during the refurbishment "because that would have delayed and made the refurbishment of the block more disruptive".
The claim stems from J Smith's YouTube video, and has been picked up by several United Kingdom newspapers, though fire officials have not verified it.
The anger on the streets of London's North Kensington has been growing in the past 48 hours.
"Those who mock health and safety, regulations and red tape need to take a hard look at the consequences of cutting these and ask themselves whether Grenfell Tower is a price worth paying".
The Daily Telegraph claimed left-wing militants had been hijacking the demonstrations and deliberately spreading political fake news conspiracy theories about the blaze.