Earlier in the day, the prime minister paid a second visit to the area around the Grenfell Tower following public outcry at her snubbing of local residents on her first visit due to "security concerns".
The prime minister's effort came as investigators try to figure out how the raging inferno started at the tower in the North Kensington neighborhood of west London.
The PM had earlier visited Chelsea and Westminster Hospital to meet staff and patients who were caught up in the fire.
London firefighters are continuing the grim search after a high-rise fire that killed at least 30 people as public anger about the blaze continues to grow.
Central to the anger is that cheaper materials may have been used in a multi-million dollar refurbishment of Grenfell Tower to keep costs down.
National media in London reported extensively Friday that it would have cost just 5,000 pounds (6,400 USA dollars) extra for a cladding material with better fire protection qualities.
People were demanding homes be found urgently for families made homeless by the blaze.
Harley Facades, which fitted the panels, told the BBC: "At this time, we are not aware of any link between the fire and the exterior cladding to the tower". "It's not a tragedy, it's a monstrous crime".
Police Commander Stuart Cundy said Saturday that this number, which was based on reports from the public, may rise. Scotland Yard has opened a separate criminal investigation. It will be undertaken by a number of specialist detectives using expertise and specialism from other organizations where required.
"The conditions within Grenfell Tower are particularly hazardous".
"We have colleagues in there as we speak, searching for and recovering those that have died".
"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected".
There have been demands for answers as to how the blaze was able to engulf the 24-storey building, trapping many on the upper floors, along with complaints that not enough was being done to provide assistance for people left homeless or information about those still missing.
"The scale of this tragedy is clearly proving too much for the local authority to cope with on their own", Mr Khan said in an open letter to Ms May.