The fire began before 01h00 on June 14th. 40 fire engines and at least 200 firefighters along with 20 ambulance crews had been called to the blaze in Grenfell Tower, which has 120 flats.
London Fire Commissioner Dany Cotton told reporters she could not yet confirm the number of deaths, due to the complexity and size of the building.
"This is an unprecedented incident. In my 29 years of being a firefighter I have never ever seen anything of this scale," she said.
The London Ambulance Service said 30 people had been taken to five London hospitals.
The 27-storey tower, containing 120 flats, is managed by the Kensington and Chelsea Tenant Management Organisation (KCTMO) on behalf of the council.
Witness could hear screaming from the upper floors as the flames rose and one desperate resident could be seen waving a white cloth.
The apartment block was built in 1974./.