Police commander Stuart Cundy said there were six confirmed fatalities, adding that the figure was likely to rise "during what will be a complex recovery operation over a number of days".
Police say there may still be people in the building who are unaccounted for.
Following the incident, the London Fire Brigade tweeted: "Crews continue to work hard at tower block fire in North Kensington Fire is from 2nd to top floor of 27 storey building".
"This is an unprecedented incident", Fire Commissioner Dany Cotton told reporters.
"The telling thing this morning is that when I woke up I wasn't surprised". Fire chiefs said it was too early to speculate on the cause of the blaze.
Local residents said they had warned repeatedly over fire safety in the block.
One said a baby was dropped from the ninth or 10th floor, another that she saw a five-year-old boy dropped from a fifth or sixth floor window.
Ruks Mamudu, 69, said she ran to safety down one flight of stairs to the ground floor from her apartment wearing only her purple pajamas and bathrobe.
"He obviously couldn't find an escape route and he couldn't leave", she said.
It was not clear if there were residents trapped, but people at the scene spoke of not being able to reach friends and family who had been inside.
Eyewitnesses said they saw lights - thought to be mobile phones or torches - flashing at the top of the block of flats, and trapped residents coming to their windows - some holding children.
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But Turkish Foreign Minister Mevlut Cavusoglu will visit Qatar on Wednesday for talks with the emir, the foreign ministry said. The newspaper said that "Saudi Arabia is exerting heavy pressure on African countries to sever relations with Qatar".
Nassima Boutrig, who lives opposite the building, said she was awakened by sirens and smoke so thick that it filled her home as well. The London Fire Brigade said it had rescued "large numbers" of people.
Cllr Bob Price, Leader of the Council, said: "My heart goes out to all those affected by the tragic fire in West London". It was fire up, up, up. "You can't get away from a fire on the 18th floor, but God's grace, they got away".
The local council of Kensington and Chelsea, which owns the block, said it was focusing on supporting the rescue and relief operation. "I just hope they have got everyone out", he said.
Other witnesses described a white, polystyrene-type material falling like snow from the building as it burned.
In the early hours of this morning a fire broke out at the Grenfell Towers in the Latimer road area of London.
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.
The block had recently undergone an 8.7 million pound ($11.08 million) refurbishment of the exterior, which included new external cladding, replacement windows and curtain wall facades.
A website run by the "Grenfell Action Group" said residents of the tower had expressed concerns over the safety of the building, specifically pointing to fire risks.
"The potential for a fire to break out in the communal area on the walkway does not bear thinking about as residents would be trapped in the building with no way out", it said. The tenants' organization's July 2014 newsletter said Grenfell "was designed according to rigorous fire safety standards".
It recommended that in case of a fire in the building residents should stay inside their apartments.
As firefighters were still searching for survivors of Wednesday's devastating high-rise fire in the west of London, there were immediate questions about whether the multi-fatality incident could have been prevented if simple safety measures had been in place.
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