The cause of the fire is unknown at time of publication.
Several hundred people are thought to have been in the block when the fire was reported at 1.15am on Wednesday, and the Metropolitan Police has confirmed six deaths and warned that the death toll is likely to rise.
London's Ambulance Service said 30 people were taken to five London hospitals, with some being treated for smoke inhalation.
A woman runs near paramedics working at a huge fire at the Grenfell Tower.
."The fire just raged on and and all of us were praying that the building would not collapse as it is in the midst of a densely populated area".
Other witnesses described a white, polystyrene-type material falling like snow from the building as it burned.
Grenfell Tower underwent a two-year £10m refurbishment as part of a wider transformation of the estate, that was completed last year.
"There's a fireman shouting "get down the stairs", one of the block's residents, Michael Paramasivan, told BBC radio. The flames have subsided significantly since the fire was extinguished at 5 a.m., but the building is still smoldering. Help! Help!' The fire brigade could only help downstairs. When he stepped out there was suddenly smoke everywhere, the whole corridor was engulfed.
"The cladding went up like a matchstick".
A residents' action group said its warnings about safety had fallen on "deaf ears".
"I just hope they have got everyone out".
Survivors were still reportedly being pulled from the block nine hours after the blaze started.
The firefighters were battling to rescue people trapped inside the tower block in west London, The Guardian reported.
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Pictures from the scene showed flames engulfing the block and a plume of smoke visible across the capital, while others showed residents looking out of windows.
Investigators were working to establish the cause of the blaze.
"It's a question of establishing how many were in there at the time of the fire".
"I am very sad to confirm that there have been a number of fatalities, I can not confirm the number at this time due to the size and complexity of this building".
Hanan Wahabi, 39, said she escaped with her husband, 16-year-old son, and eight-year-old daughter, but feared for her brother and his family who live on the 21st floor. "We kindly ask that the public stay away from the area", Cundy said. But the smoke covered them and then the fire destroyed everything.
Were there warnings something like this could happen?
The number of dead is not yet known as the horror continues to unfold in front of those residents who were lucky enough to escape the 24-storey block in west London.
Grenfell Tower was recently upgraded at a cost of 8.6 million pounds ($11 million), with work finishing in May 2016. It's a mixed-development property that houses a boxing gym and a nursery, according to a news release a year ago from the Royal Borough of Kensington and Chelsea. "There are people in their windows, putting their heads out".
As numerous residents left the block in their nightwear, nearby St Clements Church is appealing for spare clothes, toiletries and toys.
That number is 0800 0961 233.
Cotton said the building's structural integrity was being monitored and it was stable enough for fire crews to work inside. The high-rise, Grenfell Tower, is home to around 600 people, according to the Telegraph.
More than 200 firefighters, backed up by 40 fire engines, fought for hours to try to bring the blaze, one of the biggest seen in central London in memory, under control.
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