But unlike opposition leader Jeremy Corbyn and London Mayor Sadiq Khan, who was confronted by a young boy asking, "How many children died?", May did not meet with residents and this struck locals, commentators and fellow Conservative party members as insensitive.
"She wanted an entirely controlled situation in which she didn't use her humanity," former cabinet minister Michael Portillo told the BBC. "She should have been there with the residents. You have to be prepared to receive people's emotions, and not be so frightened about people."
When asked on Thursday about why she did not meet residents or visit a local community center, May said she wanted to visit the scene of the incident to be briefed by the emergency services.
The Sun newspaper said 65 people were now feared dead or missing in the fire. London police expect the death toll to rise further but said it could take months to search the burned-out building and identify the victims.
Locals were expected to stage a protest march in Kensington, where social housing tenants live cheek by jowl with billionaires in one of Europe's richest districts, from 1400 GMT while a rally to demand justice for the victims was due in the Westminster government district from 1700 GMT.
While the disaster has prompted an outpouring of generosity, there was also anger at politicians as the charred tower was cast as a deadly symbol of a divided society where the poor are neglected and the rich pampered.
"NOW THE ANGER"
British newspapers, including those which backed May in the June 8 election, sharpened their criticism of the government. They cited a series of unanswered issues including whether the cladding used on the building helped the blaze spread.
Planning documents detailing the refurbishment of the block did not refer to a type of fire barrier that building safety experts said should be used when high-rise blocks are being re-clad.
"Now the anger - furious locals demand answers," was the headline in The Sun, while The Daily Telegraph ran with "Sorrow turns to anger" under a picture of two girls in an emotional embrace.
May also drew criticism for seeming wooden and reluctant to engage in open debate with political rivals and voters during her election campaign, but local government minister Sajid Javid, responsible for housing policy, defended her on Friday.
"What she wanted to do was to speak to the people working on the ground on the recovery operation, the rescue operation to make sure that they've got everything they want and see how she could help," he told Sky news.
May failed to win an outright majority in the snap election and is now battling to strike a deal with Northern Ireland's Democratic Unionist Party to support her government.
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