Queen Elizabeth and her grandson Prince William visited a community center Friday where some of the survivors are being housed, and where volunteers have been inundated with donations of clothes and food.
The attempt to quell the growing anger over her response to the fire comes as May is under unprecedented pressure following her party's loss of its parliamentary majority last week in the country's general election.
In a letter she said: "Today is traditionally a day of celebration".
A second protest began later at Britain's Home Office, which oversees fire prevention and policing nationally.
May was heavily criticised for visiting Grenfell Tower the day after the fire, but speaking only to fire and police chiefs rather than victims and survivors.
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. The protesters eventually made their way to busy Oxford Circus, where they staged a sit-in. Hundreds of others have been left homeless and dozens are missing.
Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people "if there is evidence". They examined the apartment where the fire started and determined "there is nothing to suggest the fire was started deliberately". No sprinkler system was installed.
Services on the London Tube railway line that runs above ground close to the tower were suspended Saturday due to the "short-term risk of some debris falling onto the tracks", London Fire Brigade said.
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London's fire department says that the reason for the subway closure near the high-rise fire disaster is because of a "short-term risk of some debris falling onto the tracks".
The Royal family then travelled back to Buckingham Palace where they gathered on the balcony for an RAF fly-past. "I will help you from up there".
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.
Mohammad and his brother Omar, both students, lived together on the 14th floor.
That is why I ordered a public inquiry, with the costs for providing victims with legal representation met by government. But the government has been criticized for failing to act on recommendations from previous tower block fires.
Theresa May, Britain's embattled Prime Minister, is facing criticism for failing to meet residents when she visited the scene Thursday. Three women and three children died.
Anger has focused on why the government didn't do enough to tighten fire regulations in recent years and local people have also accused authorities of suppressing the true death toll, an idea that has spread on social media.