May, who has faced criticism of her response to the tragedy in which at least 30 people died, will meet victims, volunteers and community leaders, a Downing Street spokesman said.
“The prime minister is this morning chairing a cross-government meeting to ensure everything possible is being done to support those affected by the Grenfell tragedy,” the spokesman said.
“Afterwards, she will meet a group of residents, victims, volunteers and community leaders in Number 10.”
Queen Elizabeth II said Saturday that Britain had been plunged into a sombre mood after the deadly London tower block inferno, as public anger swelled and dozens were still reported missing.
Furious residents heckled Prime Minister May and stormed the local authority headquarters on Friday, demanding justice for the victims of the Grenfell Tower disaster which left at least 30 people dead.
There were angry scenes at the offices of the Kensington and Chelsea council, which was responsible for managing the 1970s social housing block in a working-class enclave of one of Britain’s richest areas.
“It was a death trap and they knew it,” one person shouted as demonstrators stormed inside the offices.
0:00 May pledges rehousing Share May pledges rehousing
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said Saturday. The emergency services expect to find no more survivors.
More than 70 people reportedly remain unaccounted for and the area surrounding the tower has been plastered by distraught relatives with pictures of the missing, from grandparents to young children.
Resolve in adversity
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.
The head of state said a saddened country was showing resolve in the face of adversity and a determination to rebuild wrecked lives.
She stood for a minute’s silence at the start of her birthday parade on Saturday.
“It is difficult to escape a very sombre national mood,” she said in a message marking the event.
“In recent months, the country has witnessed a succession of terrible tragedies,” the monarch said, referring to the fire and the recent terrorist attacks in Manchester and London.
“I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need.
“United in our sadness, we are equally determined, without fear or favour, to support all those rebuilding lives so horribly affected by injury and loss.”
0:00 Investigation launched into cause of blaze Share Investigation launched into cause of blaze
Anger at May
But besides the drive to help survivors, the sense of anger was palpable on the streets.
May was criticised for avoiding locals when she visited the burnt-out shell of the 24-storey tower on Thursday and faced cries of “Shame on you” and “coward” when she returned the following day.
Dozens of police officers held back booing crowds and broke up scuffles as her car drove off from a local church, where she had met survivors, residents and volunteers.
In a television interview, she sidestepped questions over whether she had misread the public mood.
Protesters marched to the edge of the police cordon around the tower, shouting “no justice, no peace”, where a few young men tried unsuccessfully to break through.
Another demonstration took place outside May’s Downing Street office, while hundreds of mourners later gathered near the tower for a candlelight vigil.
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.
First Secretary of State Damian Green, May’s deputy, said the prime minister was “distraught” and shared “the same degree of sympathy and horror” as everyone else.
He told BBC radio that the inquiry would have interim reports and “we want the response to be as fast as possible”.
Green said the government would pay for residents’ legal representation at the inquiry and reiterated May’s promise to rehouse those displaced by the fire within three weeks as close as possible to home.
Protesters stand in the lobby of Kensington town hall in west London, the headquarters of the Royal Borough of Kensington and Chelsea (AAP)AAP
Desperate survival attempts
There are questions about why the block was not fitted with sprinklers or a central smoke alarm, and whether a recent refurbishment, including new external cladding, helped fuel the flames.
The fire forced residents to flee through black smoke down the single stairwell, jump out of windows or even drop their children from the 120-apartment building.
One of the victims was Mohammed Alhajali, a 23-year-old Syrian refugee who came to Britain in 2014 with his brother and was studying civil engineering.
A second victim named Friday was Khadija Saye, a 24-year-old photographer who had exhibited at the Venice Biennale.
Seven Moroccans are among the dead, the north African country’s foreign affairs ministry said.
Police have said the recovery process could take weeks, and warned some of the bodies may be too burned to be identified.
Pope Francis sent a message of “heartfelt condolences”, in which he invoked God’s blessings of “strength and peace” on the local community.
Syrian refugee victim
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