Around an hour later the London Fire Brigade also tweeted that the whole building was in flames, starting from the second floor.
There are 120 homes in the tower block, with several hundred people thought to be in the block when the blaze began.
The area neighbours the wealthy district of Notting Hill.
Metropolitan Police said earlier that two people were being treated for smoke inhalation.
The causes of the fire, one of the biggest in London in memory, were not immediately known.
"I've never seen anything like this". One of his daughters was hospitalized.
The ambulance service said 64 people had been hospitalised, 20 of whom were in a critical condition.
40 fire engines were on the scene, the London Fire Brigade confirmed via Twitter.
At that time, most of its residents were fast asleep. It was, she said, a choice between jumping and suffering multiple broken bones, or staying and perishing in the blaze. "I hope people will understand that the priority of the Government at the moment is to manage the emergency response, to deal with the security, to deal with lives to be saved, lives to be rebuilt, and to make sure that we have got the support in place for this emergency response".
The first fire crews arrived at the scene within minutes, and the London Fire Brigade soon declared it a major incident. "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". It is not clear if people are trapped inside.
Adi Estu, 32, who was in her pyjamas and a coat, said: "I saw people flashing their lights for help, families flashing their mobile phones like a torch".
Some desperate residents threw their children from high windows, hoping someone on the ground would catch them.
But, the fire seemed to tear up the building from the outside, gutting the outer apartments and blackening most of the facade.
We were watching people dying.
I regularly sit in meetings with fire safety professionals, and their fury and frustration at the inaction of local councils and social landlords is palpable.
By mid-morning, an acrid smell permeated the area.
Desperate appeals have been made by friends and family of people who are still unaccounted for. Some were still in their pajamas, having fled in a panic hours earlier. Volunteers handed out bottled water. It's just a short walk from Kensington Palace. One resident said the fire alarm did not go off. "This was just done to tart it up and match the nearby building".
The Grenfell Action Group posted an update on its blog Wednesday, following the fire.
These are problems ordinary people have no power to solve, but already there are powerful accounts of how they reacted as the fire took lives and homes.
The management company had no immediate comment.
Local councilor Robert Atkinson told CNN the renovation works had modernized the building.
Blazes in tower blocks are rare, but each, especially those that lead to fatalities, should add to the learning used to maintain safety in buildings of similar design.
"These questions are really important questions that need to be answered", Khan said. "Clearly there's a lot more work to do to actually evacuate the building and to establish how safe it is".