An earlier report said that at least 600 people were believed to have been inside the flats when the fire began.
The fire brigade said the fire had spread throughout the entire building, now covered in plumes of smoke with visible pockets of fire within the charred structure.
The fire at Grenfell Tower on the Lancaster West Estate was reported at 01:16 BST and about 200 firefighters are tackling the blaze.
Two hundred firefighters were on the scene but Jodie said they struggled to reach those inside the building, who were unable to leave.
He said emergency centres have been set up for evacuated residents, and that the council is "providing as much support as we can".
This story has been corrected to show that the building has 24 floors, not 27.
Smoke and flames engulfed Grenfell Tower on Wednesday morning.
Firefighters battled a massive fire in a 27-floor high-rise apartment building in west London for several hours Wednesday.
"In my 29 years of firefighting I have seen nothing of this scale", Cotton said.
"She said her friend jumped".
"I can not confirm the number at this time due to the size and complexity of this building, and it would clearly be wrong for me to speculate further".
There is likely to be an extensive inquest.
More than 20 ambulance crews were sent to the scene, London Ambulance Service said.
London Mayor Sadiq Khan said a "major incident" had been declared in response to the blaze.
There were fears that the building, which houses more than 100 apartments, might collapse.
"I'm really not in any position to answer any questions about the structure". I woke up my auntie who was sleeping, it was about 1.15am, and we started to make our way down.
"It's just horrendous. I'm just hoping there's not too many dead".
However, RBKC said in a statement that "Local Authority Liaison Officers are working directly with emergency services at the scene" and that "at present all our focus is on supporting the rescue and relief operation".
The cause of the fire was not immediately known. We came outside and were confronted with the building that was completely engulfed in flames.
Residents are still trapped inside the building.
A woman who lived near the building said people could be heard screaming as the blaze quickly spread.
"There were people banging on windows screaming, crying out for help".
"It was everywhere, it was like snow", she said.
"We could hear people screaming, "Help me, help me", and flashing their phone lights to let people know they were there. The whole of his window was on fire".
"They said it was fine - it's not fine", she said.
"People can be seen at the windows, including one man waving a blanket from the window", a witness told The Guardian.
"We kindly ask that the public stay away from the area".
Michael said he had escaped in his boxer shorts through smoky corridors carrying his daughter wrapped in a dressing gown.
Those forced to flee their homes described hearing their trapped neighbours' screams. "It was just unbelievable how quick it was burning".
Samira Lamrani, a witness, said a woman dropped a baby from a window on the ninth or 10th floor to people on the sidewalk.
London's Metropolitan Police said a number of people were being treated for a range of injuries, but did not provide more specifics.