Confirming the latest death toll, Metropolitan Police commander Stuart Cundy said the tower remained "in a very hazardous state" but there was "nothing to suggest at this time that the fire was started deliberately".
Commander Stuart Cundy of the Metropolitan Police told a press conference the number may change but those believed to have died when the London tower block went up in flames is now in double figures.
The death toll had previously stood at 30 and officials added that it would likely take weeks for all the bodies to be recovered and some may never be identified.
On the figure of 58, he said: "I really hope it won't, but it may increase", while adding that "it might be that some of those are safe and well", and for some reason, had not yet made themselves known to the police.
In a separate rally at Whitehall, more than a thousand people marched to Downing Street in anger at the Government's response to the disaster.
He promised an exhaustive investigation into the fire which would include scrutiny of the renovation works on the block which some experts believe may have left the building more vulnerable to the catastrophic blaze.
Asked repeatedly whether she had misread the public mood, May did not answer directly but said the focus was on providing support to the victims.
The meeting is unlikely to quell complaints that May has been slow to reach out to fire survivors, despite her announcement of a $6.4 million emergency fund to help the displaced families.
At least 45 fire engines and over 200 firefighters and officers were deployed to the scene, the London Fire Brigade said.
One of her closest allies, Damian Green, defended May, saying she was "distraught about what has happened". "I absolutely get why they're angry".
Scalise upgraded from 'critical' to 'serious' condition
Before James Hodgkinson left his home in Belleville, Ill., in March, he sold almost everything he owned from his businesses. Bailey was spotted Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
As the Grenfell residents and volunteers passed through the gates of Downing Street, protesters shouted angry chants about the Prime Minister and wore white ribbons as a sign of solidarity.
Queen Elizabeth and her grandson Prince William visited a community centre Friday where some of the survivors are being housed, and where volunteers have been inundated with donations of clothes and food.
"It is hard to escape a very sombre national mood", Elizabeth said in a message on her official birthday.
"Put to the test, the United Kingdom has been resolute in the face of adversity", the queen wrote in her message. "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".
Such a direct message from the monarch is rare and indicated the extent of the turmoil in Britain.
Her failure to win a majority in an election she did not need to call had already sparked a tumultuous week and pitched Britain into its deepest political crisis since the Brexit referendum a year ago.
"Wallowing in the wash of a general election that stripped our prime minister of her authority on the very eve of European Union negotiations, neither common sense nor the evidence suggest she can re-establish public confidence", Parris wrote in the Times.
This was Prime Minister's second meeting with those affected by Wednesday morning's fire, which was described as "unprecedented" by London's Fire Brigade Commissioner.
"This prime minister is not viable".