Police Commander Stuart Cundy said the number of 58, which was based on reports from the public, may rise and includes the 30 deaths that have already been confirmed.
"People raised these concerns, people were expressing issues regarding the safety and unsafe living conditions", says Lancaster West Residents Association chairwoman Olesea Matcovschi.
Emergency workers walk on the roof of the fire-gutted Grenfell Tower in London, Friday, June 16, 2017, after a fire engulfed the 24-storey building on Wednesday morning.
British Prime Minister Theresa May, facing criticism for the government's handling of the disaster, met Saturday with a small group of fire survivors invited to her official residence at 10 Downing Street.
Rania, 30, was trapped on the 23rd floor of the Grenfell Tower along with her two children Fathia, aged five, and Hania, aged three. "I said 'why you didn't come - they brought us outside, I thought you are with us.' He said 'no one brought me outside.' He said, 'why you left me?'"More news: ICC Champions Trophy: India-Pakistan clash bigger than Ashes: Irfan Pathan
"What I'm now absolutely focused on is ensuring that we get that support on the ground", May said in a BBC Newsnight interview.
Survivors of the building claimed the fatal fire resulted from a lack of maintenance to the tower.
Earlier, a sign at a Tube station said that the service suspension was because of the "safety" of nearby Grenfell Tower, suggesting structural concerns.
"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.
Another demonstration took place outside May's Downing Street office, while later in the evening, hundreds of mourners gathered near the tower for a candlelight vigil.
Two neighbouring Tube lines are to be partly suspended into a second day amid safety concerns of debris falling on to the tracks.More news: UK Government 'absolutely steadfast' in commitment to peace process - Theresa May
Although the flames have now been extinguished, Cundy said rescuers don't expect to find any survivors inside the building at this point.
According to police, 58 people are missing and presumed dead in the fire, though they say this number could change.
The Trooping the Colour - a large parade of soldiers that march through central London - marks the Queen's official 90th birthday. Construction company Rydon made the refurbishment of the block worth Rs 8.7 million pound and was completed in July 2016.
May has announced a judge-led inquiry into what happened, and on Friday promised £5 million ($6.4 million, 5.7 million euros) for emergency supplies, food and clothing.
The government is expected to discuss the establishment of a strike force to urgently identify fire-prone buildings at a meeting on Monday, The Daily Telegraph reported. "This year, however, it is hard to escape a very somber national mood".
"There's a need for the public to hear you say in words of one syllable: 'Something awful has happened; something has gone badly wrong".More news: Mastermind behind Iran attacks killed, 50 arrested
Queen Elizabeth II said the disaster had cast a sombre pall over Britain, but insisted the country was showing resolve in the face of adversity. "United in our sadness, we are equally determined, without fear or favor, to support all those rebuilding lives so horribly affected by injury and loss".
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