"The bodies have been taken to a morgue, but more bodies remain in the building".
He added that there was nothing to suggest that the fire - which has also left 24 people in hospital, with half of those still in critical care - was started deliberately.
The cause of the fire is under investigation, and authorities refuse to speculate on what could have started the blaze.
Fire safety engineers were stunned at the pace with which flames tore through the 120-apartment Grenfell Tower in the early hours of Wednesday when most of the 600 residents were asleep.
While 30 people have been confirmed dead, there are fears the death toll could hit hundreds. "There is a risk we may not be able to identify everybody".
"It's wrong if there is a delay because people are living in thousands of tower blocks all around the country and they need to know the lessons are going to be learned quickly", she said.
They met volunteers, local residents and community representatives while visiting Westway Sports Centre in west London, near the burnt down 24-storey Grenfell Tower.
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Prime Minister May faced much criticism for meeting fire brigade and police officials at the disaster site, but not victims.
"Every single person living in a high-rise building today will be frightened, will be traumatised and will be very, very anxious".
Grenfell Towers was a low-income housing unit, and most of the people who died were people of color, many of them Muslim. The Independent reported that those up early for Ramadan may have saved more lives when it came to spreading word and evacuating people from the building.
"I spoke to one of my officers who was very near when someone came out the window, and he was in tears and he is a professional fire officer", Cotton told Sky News.
May spent nearly an hour speaking to patients and staff at London's Chelsea and Westminster Hospital on Friday, a day after visiting the scene of the blaze in west London to talk to firefighters, police and other emergency workers. She said she had lived on the 10th floor of the building for 31 years.
Theresa May has been chased out of Kensington by an angry crowd shouting "coward!" and "shame on you!", as she was bundled into her auto amid growing anger over the Grenfell Tower fire. The probe was launched when it emerged that cladding panels similar to those believed used in Grenfell Tower have been banned on tall buildings in the US.
The angry protesters barged their way through an automatic door at Kensington and Chelsea town hall and sought to gain entry to an upper floor.
The first of the dead to be identified was Mohammed Alhajali, a 23-year-old refugee from Syria who had lived in London since 2014. "Between apartments there is meant to be enough layers of plaster board to provide for one hour fire resistance".
More than £1 million has been raised to help those affected by the fire, with more than 60 tonnes of donations collected by one local mosque.