Forty fire engines and 200 firefighters and officers were called to the scene.
Firefighters at the scene said they had managed to evacuate residents up to the 11th floor.
The Metropolitan Police confirmed on Wednesday evening that 12 people died in the blaze, adding that the figure was "likely to rise".
People on the ground were heard calling to those inside to shout out their unit number for rescuers.
"We've lost a lot of people".
Residents who escaped spoke of others trapped and screaming for help, with some throwing children from windows and others jumping from upper floors.
Lamrani said: "People were starting to appear at the windows, frantically banging and screaming".
Ruks Mamudu, 69, escaped from her first-floor apartment wearing only her purple pyjamas and bathrobe.
Some witness reports say children and a baby were seen being thrown out of windows amid the blaze.
A fire and rescue service earlier said the building had 27 floors.
Prime Minister Theresa May said she was "deeply saddened" by the incident.
A witness to the Grenfell Towers fire has been arrested after he allegedly took pictures of a dead body and posted the images on Facebook.
The group claimed access to the building was "severely restricted" for emergency services and other vehicles and residents were advised to stay in their flats in case of fire.
Some were fortunate to make it out on their own, including Mickey Paramasivan, who was nearly asleep when he smelled burning plastic.
A 2014 KCTMO newsletter issued during regeneration work said the building's "longstanding "stay put" policy stays in force until you are told otherwise". "The more I looked up, floor upon floor". But London police commander Stuart Cundy told reporters he did not believe further survivors would be found in the building.
Another witness, Hanan, who gave only her first name, told ABC News that she managed to escape from the building's ninth floor and that she was anxious about her brother, Abdul Aziz, and his family, who were on the 26th floor.
Refurbishment of the housing block had been completed past year and the Fire Brigades Union said something had gone badly wrong with fire prevention procedures at the building.
Burning debris cascaded from the blazing building. We will be soon making contact with next of kin.
Bernie Sanders says man ID'd as shooter was on campaign
Hodgkinson was, however, arrested in 2006 for assaulting his girlfriend, according to NBC News investigative reporter Tom Winter. The paper posted a photo Wednesday of Hodgkinson carrying a placard and protesting against the Republican Party in 2012.
Golden State Warriors Reclaim NBA Championship Title
When it came time to reflect on the series, Cavaliers coach Tyronn Lue pointed to the final 2:13 of Game 3 as the difference. Durant won the Finals MVP award after averaging 35.2 points, 8.4 rebounds, 5.4 assists, and 1.6 blocks for the series.