Some people were reported to have jumped from the building while witness described seeing people, including children, banging on windows, screaming and crying for help.
Reports said an evacuation process was under way amid fears that the building could collapse.
The cause of the fire was not known at this stage, London Fire Brigade said.
A thick plume of smoke could be seen for miles around, while witnesses reported people jumping from open windows near the top of the 24-story building after being trapped by the advancing flames.
People at the scene spoke of being unable to reach friends and family inside. "Whoever is at the top of (the tower), I pray to god they got out". "There were a lot of people hanging out of the windows, screaming, crying for help", he says "There was this one window where they'd tied bedsheets together to make a makeshift rope-two people were hanging off the rope".
"I saw the news and felt like we had to do something", she said.
Another witness said a family friend was "stuck on the eighth floor with her 5-year-old daughter" until 5 a.m., nearly four hours after the fire broke out. It was fire up, up, up.
He woke his children up, handing them wet towels, and they escaped through the fire well. "Us members of the public were reassuring them, telling them we've done what we can and that we've phoned 999, but obviously the look on their face was death", Lamrani said. More than 50 people are being treated in hospital. He says there was heavy smoke in the hallway and he couldn't find the stairs.
Khalid Ahmed, a 20-year-old student who lived on the eighth floor, was playing video games when he smelled smoke.
She then wrote: 'Guys I don't know what to do. Volunteers handed out bottled water. "Questions need to be answered as soon as possible", said London mayor Sadiq Khan.
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Mr Harris suspended his inquest into all the deaths until police are able to complete their investigation into the attacks. Mr Harris told the families: All of our thoughts and condolences are with you at this awful time.
In a statement on Facebook, assistant commissioner Dan Daly said: "Firefighters wearing breathing apparatus are working extremely hard in very difficult conditions to tackle this fire".
Actor and writer Tim Downie, who lives nearby, said: "It's horrendous". The whole building is engulfed in flames.
"It's the most terrifying thing I've ever seen".
"I think everyone felt really helpless because no-one could get to them".
"It is our conviction that a serious fire in a tower block or similar high density residential property is the most likely reason that those who wield power at the KCTMO will be found out and brought to justice!" a residents organization, the Grenfell Action Group, wrote in a blog post previous year.
The building was refurbished recently at a cost of £8.6 million, with work completed in May a year ago.
Watching breaking news about the Grenfell Tower fire catastrophe.
Concerns about the safety of the building were raised as early as 2012, when a health and safety review found fire safety equipment had not been checked for up to four years.
A residents' action group said its warnings about safety had fallen on "deaf ears".
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