Sniffer dogs are to be sent in to search for evidence and identification of people still inside.
The Queen has said her "thoughts and prayers" are with families.
People have been desperately seeking news of missing family and friends.
More than 30 people remain in hospital - 17 of whom are in a critical condition.
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00:48
Many more people are unaccounted for as fire crews continue to tackle the blaze in west London.
Firefighters and police were searching through the still smouldering debris of a tower block inferno in London to retrieve bodies as police warned the death toll of 12 would rise in the coming hours.
Hundreds of people have made desperate calls to a specially created casualty bureau to report missing loved ones in the aftermath of the blaze, which ripped through the 24-storey Grenfell Tower in west London.
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14:37
Met Police confirms six people have died with figure 'likely to rise'; more than 50 in hospital
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13:40
Deaths were confirmed early Wednesday after a blaze ripped through a high-rise apartment block in the British capital as residents slept. At least 50 people were injured, according to authorities.
More than 250 firefighters battled the inferno at Grenfell Tower through the night. Witnesses told of hearing people calling for help from within the building as flames quickly spread upwards.
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11:44
The Metropolitan Police also said there are fatalities among Grenfell Tower residents, asking Londoners to contact the Casualty Bureau to get information on their loved ones. “It is likely to take some time before we are in a position to confirm the cause of the fire," police said in a statement.
The number of people receiving medical care has risen to 50, the London Ambulance Service said. Earlier, the fire commissioner and Metropolitan police confirmed that there are fatalities, though the exact number is yet to be established.
London Fire Commissioner Dany Cotton said in a preliminary statement there have been a number of fatalities following the Grenfell Tower fire. At this stage, she said, it is impossible to report the exact number of those killed in the fire due to the size and complexity of the building. The cause of the fire has also not been established.
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10:16
A nightmarish aerial image of the Grenfell Tower fire has been published by Sky News, with plumes of smoke spreading all over the neighborhood.
The London Fire Brigade has also posted a photo showing the top of Grenfell Tower burnt out, with the blackened walls in flames.
Areas around the Grenfell Tower have been cordoned off and around 30 adjacent flats have been evacuated by police, London Fire Brigade has said.
Photos and videos posted by Londoners on Twitter suggest the incident in West London is far from over, as Grenfell Tower is still burning, producing pillars of thick smoke.
People on social media say residents used bed sheets as makeshift ropes to escape the building.
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09:46
Some residents evacuated from the tower are being taken care of at several makeshift shelters. Saint Clement Church and Saint James Church, located near Notting Dale, Notting Hill, North Kensington, and Holland Park, are receiving evacuees, local people say on Twitter.
London Mayor Sadiq Khan said 200 firefighters and 20 vehicles were dispatched to the scene. He also confirmed he is in close contact with all services called in to deal with the emergency.
The London Ambulance Service says is has taken 30 patients to five adjacent hospitals following the fire in West London, and 20 ambulance crews as well as trauma and hazardous area response teams are now operating in the vicinity of the Grenfell Tower.
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09:29
Several videos of the massive fire in London show residents shouting for help and jumping out of the building. The fire engulfed the 27-storey Grenfell Tower on Latimer Road, west London, early Wednesday.
Images and videos shared on social media show residents desperately asking for help, while a crowd watches the massive fire engulf the apartment block. According to reports, the fire spread from the second floor to the top floor of the building on Wednesday.
Watch the video of the horrifying fire incident below:
Eyewitness accounts have been pouring in, with reports claiming women and children were among those trapped on the burning floors.
***
09:10
Massive flames licked up the sides of the block as 200 firefighters battled the blaze along with 40 fire engines. Flumes of black smoke billowed into the air.
London Fire Brigade said the fire had engulfed all floors from the second to the top of the Grenfell Tower on the Lancaster West Estate in west London.
Some people were trapped in the fire, with residents desperately shouting for help from windows on upper floors as the fire spread, some British media reported. Reuters could confirm those reports.
"A number of people being treated for a range of injuries," police said. "Residents continue to be evacuated from the tower block fire."
The cause of the fire, which broke out just after 0000 GMT, is not known at this stage, the Fire Brigade said.
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