The fire was reported at the 24-storey block, Grenfell Tower, in north Kensington, 00:54 BST.
It is believed to have started on the fourth floor and spread quickly.
Forty fire engines and around 250 firefighters went to tackle the blaze.
Theresa May said there would be a full investigation and "if there are any lessons to be learned they will be".
Twelve people have died, according to police, with the number expected to rise.
The London Ambulance Service says 78 people have been treated in six hospitals - St Mary's, Chelsea and Westminster, Royal Free, St Thomas', Charing Cross Hospital and King's College Hospital.
Thirty-four patients remain in hospital of which 18 are in critical care.
Firefighters rescued 65 people from the building, according to the London Fire Brigade. Others made their own way out.
It is unknown how many people remain unaccounted for, with police saying that it is unlikely that more survivors will be found.
London Fire Commissioner Dany Cotton said a "number" of firefighters had suffered minor injuries.
Eyewitnesses said some people may have been trapped in the building, which contains about 120 flats.
Notting Dale ward councillor Judith Blakeman, who lives across the road from the block, said between 400 and 600 people live in the building.
London Mayor Sadiq Khan said fire crews only managed to reach the 12th floor at the height of the fire.
A firefighter directs a jet of water at a tower block severely damaged by a serious fire, in north Kensington, West London, Britain June 14, 2017. [Photo/Agencies]
A baby was caught by a member of the public after being dropped from a window as fire engulfed London's Grenfell Tower, a witness has said.
Samira Lamrani said she saw a woman gesturing to the crowd below that she was about to drop her baby from "the ninth or 10th floor" of the building.
A man ran forward and managed to catch the baby, she said.
She described seeing people "from all angles, banging and screaming for help" from the tower block.
"We were reassuring them, telling them we've done what we can and that we've phoned 999, but obviously the look on their face was death."
She said one resident attempted to use a "homemade parachute" to lower himself out of a window.
Ms Lamrani said there were "endless numbers of people" trapped in the building, including children, and she could hear them "screaming for their lives".
It is not yet known what caused the fire.
Matt Wrack, general secretary of the Fire Brigades Union, said "a full investigation will need to be undertaken at the first possible opportunity".
Grenfell Tower is on Latimer Road, in west London.
It's part of the Lancaster West Estate, a social housing complex of almost 1,000 homes, in the borough of Kensington and Chelsea.
The tower block is near Westfield shopping centre in White City and the A40 - a major route for traffic entering and leaving the west of London.
Grenfell Tower was built in 1974 by Kensington and Chelsea Borough Council.
An £8.6m refurbishment - which was part of a wider transformation of the estate - was completed by Rydon Construction in May last year. Work included new exterior cladding, replacement windows and a communal heating system.
There was also extensive remodelling of the bottom four floors, creating nine additional homes, and improvements to communal facilities.
Rydon said it was "shocked to hear of the devastating fire" adding that the work "met all required building control, fire regulation and health & safety standards".
It later issued a new statement, removing the previous mention of the building meeting fire regulation standards, instead saying the project met "all required building regulations".
The local Grenfell Action Group had claimed, before and during the refurbishment, that the block constituted a fire risk and residents had warned that access to the site for emergency vehicles was "severely restricted".
In February 2013 residents warned fire safety equipment, including fire extinguishers, had not been tested for 12 months.
KCTMO said it was aware that concerns had been raised historically by residents and they will form part of its investigations.
Plasco building, Iran, January 2017: A fire at a 17-storey commercial building in the Iranian capital led to multiple deaths, including 18 firefighters. The building collapsed - it had been deemed unsafe prior to the incident.
Baku, Azerbaijan, May 2015: 16 people died in a fire in a residential building, including five children - cladding on the outside of the building was blamed for the way the fire spread.
The Torch, Dubai, February 2015: Fire swept through one of the tallest residential buildings in the world. Hundreds of people had to be evacuated from the 79-storey skyscraper.
Krasnoyarsk, Russia, September 2014: A 25-storey tower block was destroyed by fire. All 115 residents fled the building and there were no reported casualties.
Shanghai, China, November 2010: A fire in a 28-storey tower block killed 53 people and injured at least 90. Chinese media reported that unlicensed welders were blamed for the accident.