The death toll is unclear - and rising.
No one has said exactly where the fire started.
Speaking after, Mrs May told Sky News: "What I want to talk about today is what the Government is making available to the victims of this absolutely horrendous tragedy, I think we were all when we saw the horrific scenes that had happened at Grenfell Tower..."
The exterior cladding and the insulation squeezed between its panels were added as part of an extensive renovation completed past year. The renovation included the cladding of the entire exterior of the building, which residents have reportedly blamed for the speed at which the fire spread.
One woman said: "Someone needs to be held accountable".
The fire forced residents to flee through black smoke down the single stairwell, jump out of windows or even drop their children from the building. Cladding is clearly one of the things that has to be looked at. We need to know what happened; we need to have an explanation of this, we owe that to the families.
Messages on a wall for the victims and in support for those affected by the massive fire in Grenfell Tower, in London, Thursday, June 15, 2017.
London police say the number of victims has increased to 30 in the fire that engulfed a high-rise building.
Grenfell Tower's residents were operating under "stay put" guidance in case of a fire under the assumption that modern fire doors would protect them in their apartments until the fire department could safely get them out. The blaze ripped through the building early Wednesday, trapping many residents in their homes. "If it's compromised, something else has to be done, " he said.
A railway track which lies in the shadow of a London tower block gutted by a deadly blaze this week was closed on Saturday as the fire brigade worked to clear up debris inside the building.
Aluminum composite panels essentially consist of two thin layers of aluminum sandwiched around a lightweight insulating material.
The Grenfell Tower housed about 600 people in 120 apartments.
Britain says Brexit talks to start Monday
The talks were "productive", May told a news conference in Paris following a meeting with French President Emmanuel Macron. After dinner, the two leaders will watch a friendly soccer match between England and France.
The firm behind the work said the project met all required building regulations.
Cladding is often used because it is attractive and can be easy to clean.
The inferno Wednesday morning at the 24-story Grenfell Tower has led to community anger and protests over the government's response.
He explained how he first knew of the fire.
Cladding has played a contributing role in numerous fires worldwide, including the New Year's Eve fire at a 63-story luxury hotel in Dubai, and other severe fires in the United Arab Emirates.
The cross-Government group is coordinating the immediate and long-term response to the west London blaze, with police saying that 58 people are missing and presumed dead.
The cause of the fire has not yet been determined, though some have mentioned the explosion of an appliance could be the cause.
Within a short walk from the social housing block in west London where 17 people - and perhaps many more - died in a devastating fire are some of Britain's wealthiest streets, lined with elegant, multi-million-pound townhouses.
When the panels are installed in a continuous row without fire breaks, it can provide an air space that acts like a chimney linking the bottom floors to the top.
Residents had complained about safety for several years. There were worries about exposed gas pipes in recent weeks, and also concerns about rubbish posing a fire risk and the placement of boilers and heaters.
Labour Leader Jeremy Corbyn, who too visited the site, said separately that "the truth has to come out".
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