The fire broke out at around 1am and quickly spread through the building.
London Fire Commissioner Dany Cotton told a news conference that she has never seen anything like this before in 29 years of service.
She said: "It's a major fire that has affected every floor from the second upwards. There are 200 fire fighters. The first call came at 6 minutes before 1am. Crew with breathing aparatus have been working in extremely difficult conditions
"I am very sad to confirm there have been fatalities. I cannot say how many at this time. The cause of the fire is not known at this time."
Earlier this morning the London Ambulance Service revealed that 30 people had been taken to hospital following the fire.