In an interview on BBC's newsnight on Friday, the prime minister said the fire which has claimed the lives of at least 30 people with dozens more missing was "absolutely horrifying" and had been a "terrifying experience" for those affected.
At least 30 people have died in the Grenfell Tower fire, police have revealed.
Her government is also due to launch hard Brexit talks with the European Union on Monday.
New York City Fire Commissioner Daniel Nigro, whose department is among the most practiced in the world at fighting fires in tall buildings, says he believes in the stay-put policy but "what happened in London, in which a fire went from the fourth floor to the 21st floor in what we understand was in 17 minutes, is unprecedented".
The queen and her husband, Prince Philip, stood silently on the steps of Buckingham Palace before the start of the Trooping the Color that each year marks the queen's official birthday, which is traditionally celebrated in June when the weather is warm.
The queen said it was "difficult to escape a very somber mood" on what is normally a day of celebration. They previously estimated the figure to be 30.
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A huge fire started at the 24-floor Grenfell tower high-rise block in North Kensington on Wednesday, engulfing the entire building and trapping nearly 120 families inside.
The 24-story Grenfell Tower in the north Kensington neighbourhood in west London is near several major transport hubs.
"Sadly, it is expected that the total will rise and it is not expected that any survivors will be found", he said.
She has promised to set up a public inquiry and pledged £5 million (NZ$8.8 million) of support, housing guarantees and help with access to bank accounts and cash.
There are questions about why the block was not fitted with sprinklers or a central smoke alarm, as well as whether the recent refurbishment - including the use of cladding that was blamed for worsening previous building fires in France, the United Arab Emirates and Australia - helped fuel the flames.
Separately, hundreds of protesters stormed the local town hall chanting: "We want justice". British officials have ordered a review of other buildings that have had similar renovations.
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The FBI said that the shooter's weapons found at the scene - a 9mm handgun and 7.62mm caliber rifle - had been legally purchased. The congressman underwent another surgery Saturday, and the hospital says he is more responsive and speaking with family.
After a botched snap election that lost her party its majority in parliament, May is facing criticism for her response to the blaze which engulfed the 24-storey apartment block of social housing on Wednesday. May was jeered after she made a visit to the community Friday.
This will ensure those involved in the response to the tragedy are able "to receive targeted support should they need it", Downing Street said.
"The human cost and bad reality of what took place at Grenfell Tower affects so many people, my thoughts and those of all my colleagues remain with those so deeply affected".
Mrs May has said survivors would be consulted on the terms of reference for the full public inquiry, so they can obtain the answers they are seeking. There is ample food and water but very little privacy or proper bedding, and with the tower destroyed, no one knows where they will be relocated or for how long.
Protests were held in London on Friday as residents demanded support for those affected by the fire.
Patty Jenkins Has Not Yet Been Signed as Wonder Woman 2 Director
The Avengers and Avengers: Age Of Ultron director, Joss Whedon, took to Twitter to praise Wonder Woman and called it a "delight". Warner Bros . would be insane not to bring Patty Jenkins back, and the uproar would be deafening.