The deadly blaze is said to have started after a faulty fridge freezer exploded causing fire to spread up the 27-story block.
Witnesses said that they saw people jumping from the upper floors.
They could be heard begging for help as they leaned out of their windows and lashed bed sheets together to make rope in a frantic attempt to reach the ground.
London medics have treated 15 people for smoke inhalation and taken them to hospitals.
"There was smoke everywhere, people screaming and shouting".
Design specifications seen by the Press Association suggest the renovation work carried out at Grenfell Tower included a 50mm "ventilated cavity" next to 150mm of Celotex FR5000 insulation.
The block had recently undergone an 8.7 million pound ($11.08 million) refurbishment of the exterior, which included new external cladding and replacement windows.
The blaze was described as being like "hell on earth".
"It's like hell on earth".
"Most of the people I could see were Muslims".
Alice, a London resident who lives nearby, told The Guardian that she saw one person jump from the building while it was in flames.
He said: "If you deny local authorities the funding they need, then there is a price that's paid". Oh my goodness, it spread so quickly.
Most of the people I could see were Muslim.
The fire lit up the London sky and as it began to burn out, sent up huge plumes of smoke.
"My reaction was; "This was a tragedy waiting to happen", she told AAP".
"London Fire Brigade's Control room took multiple calls, with the first being received at 00.54am The first fire crews arrived on the scene in under six minutes and were faced with a rapidly developing and incredibly complex fire".
The Metropolitan Police has confirmed the deaths of 12 people on Wednesday and they've warned that the number will rise.
Reports of a fire at Grenfell Tower in North Kensington, west London, came in just before 1am local time on Wednesday (12pm NZ Time). Mayor Sadiq Khan said many questions must be answered about safety for the scores of other apartment blocks around the British capital.
Grenfell Tower is a 24-storey public housing block containing 120 apartments that is part of the Lancaster West Estate.
The Grenfell tenants' organization's newsletter instructs residents to stay put in a fire unless the blaze is in their own apartment or in their hallway - the same guidance used in multistory hotels and other high-rise buildings.
On Instagram, she wrote: "This is my neighbourhood I can't believe this is happening".
In a post on Instagram, Oliver wrote: "To any of the 100's of FAMILIES effected by this awful fire at Grenfell Tower Notting hill today, You are all welcome to come hang out in my restaurant and be fed and watered by my Jamies Italian team".