She also announced that she was ordering a full public inquiry into the disaster.
Following a brief, private visit to the scene, the prime minister said residents of Grenfell Tower deserve answers about how the fire spread so rapidly through the building.
The cause of the blaze is under investigation, but a tenants' group had complained for years about the risk of a fire. "We have to get to the bottom of this - the truth has got to come out and it will".
A woman is awaiting news of her friend who was caught up in a fire that engulfed the Grenfell Tower in west London, Britain, June 14, 2017.
The partial collapse of Ronan Point Tower in east London in 1968 led to an overhaul of building regulations. The couple, both architects, moved to London only three months ago.
Gottardi's father, Giannino Gottardi, told ANSA he was talking to his son as late as 4:07 a.m. (0207 GMT Wednesday; 10:07 p.m. Tuesday), "then they told us their apartment had been invaded by smoke", and the call ended.
Fears are growing that the number of people who lost their lives in the Grenfell Tower fire in west London could reach 100, as the government promises a public inquiry into the deadly incident, according to reports.
May didn't speak with journalists during the visit. "We've got structural surveyors and my urban search and rescue team who are going to come down, make an assessment and find a way of making the building safe so that we can go through the whole building, fingertip search, painstakingly, looking to see what's in there", she added.
17 dead, public investigation sought in London tower fire
An investigation into the cause of the blaze, the worst in the British capital in a generation, was underway. The Mayor of London demanded the public inquiry deliver an interim response to the disaster this summer.
Authorities have said they did not expect to find any survivors.
May faced further delays in forming her new government after a failed election gamble when her would-be allies said their agreement would be put back following the blaze.
She also said sniffer dogs were being used to locate bodies.
Built in 1974, the 24-floor building contained 120 apartments and was managed for Kensington and Chelsea Council by an independent management organization.
"It can't be acceptable that in London we have luxury buildings and luxury flats left empty as land banking for the future while the homeless and the poor look for somewhere to live".
The criminal probe was launched after it emerged that cladding, used on Grenfell Tower is banned in the U.S., and that it would have cost just 5,000 pounds extra for the contractors to apply a fire-resistant version of panelling to the building, according to a report by the Independent. May was seen at the scene talking to senior officials from the emergency services and said that she was overwhelmed by the bravery shown by the firefighters.
Firefighters said they had taken 65 people from the burning building and a total of 74 people were listed as wounded, including 18 who remained in critical condition. Some jumped to their deaths rather than face the flames, and witnesses reported seeing small children thrown from the tower by their families in a desperate bid to survive.
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