It was not immediately clear how the fire started, and the Metropolitan Police said the number of people killed will likely rise.
Mr Cundy added: "Whilst we may have accessed every floor that is not the same as a full search of the whole building, and as I said while we now sadly have 12 fatalities, I do believe that figure will rise and sadly I don't anticipate that there will be further survivors".
The fire at Grenfell Tower on the Lancaster West Estate in Latimer Road was reported at 01:16 local time.
'My friends live on the fourth floor, someone knocked on their door, they didn't know and they got out.
Samira Awil said she had seen multiple bodies, including children, covered in sheets outside Grenfell Tower where they had fallen. "There are still people in there", Samuels said.
The block had recently undergone an 8.7 million pound refurbishment of the exterior, which included new external cladding, replacement windows and curtain wall facades.
With shock, horror, sadness and heartbreak people woke up to the news that a huge blaze engulfed a tower block in west London.
Labour leader Jeremy Corbyn said "searching questions" need to be asked about what happened, suggesting spending cuts could have contributed to the deadly fire.
Boutrig said her friend's brother, wife and children lived in the building and that her friend was waiting to find out if they were OK.
Another resident, called Zara, said she saw a woman throw her son, who was about five years old, from a fifth or sixth floor window to escape the blaze. When she got downstairs there was only four of them with her.
When her daughter called a couple of hours later, the blaze was already engulfing the entire building.More news: Justices strike down gender differences in citizenship law
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Precise number of fatalities and the cause of the fire remain unknown, and many residents are still unaccounted for.
One of the recommendations made by the Lakanal House coroner was that sprinklers should be retrofitted in thousands of British tower blocks in order to combat the spread of fire.
Met Police officers arrived at the scene to assist the London Fire Brigade and the London Ambulance Service.
A July 2014 newsletter for residents said the tower building was designed "according to rigorous fire safety standards" and recommended that residents stay inside their apartments in the case of a fire.
Speaking within sight of the burning high-rise - originally white and gray, but most of which had turned a charred black - Cotton said she would not speculate on the ultimate death toll because of the "size and complexity" of the building.
He said residents had complained for years to Kensington and Chelsea Council about the building's safety, to no avail.
Children were heard screaming for help and people were jumping their balconies as the blaze quickly engulfed the building near NLadbroke Grove overnight. "A neighbour's smoke alarm went off and another neighbour phoned and told me to get out", Daffarn said.
A spokesman for Harley said the company could not comment at this stage because it did not have information about the fire.
The local council of Kensington and Chelsea, which owns the block, said it was focusing on supporting the rescue and relief operation.
"Fire is from 2nd to top floor of 27 storey building", the fire service said on Twitter.
The Grenfell Action Group, a community organization formed to oppose a nearby redevelopment project, has been warning about the risk of fire at Grenfell Tower since 2013. "We will cooperate fully with all the relevant authorities in order to ascertain the cause of this tragedy".