Witnesses reported harrowing scenes as residents trapped in top floors leaned out windows, flashing their mobile phone lights and calling frantically for help.
Police commander Stuart Cundy gave the death toll of 12 but added the figure was likely to rise "during what will be a complex recovery operation over a number of days".
The Metropolitan Police said two people were being treated at the scene for smoke inhalation and cordons were in place.
More than 200 firefighters, backed up by 40 fire engines, fought for hours to try to control the blaze, London's deadliest for a generation.
"I have seen it with my own eyes". They say their complaints were not investigated.
More than 12 hours after the fire broke out, the building was still smouldering, though the building was not in danger of collapse. Police said that the number of casualties would rise. It is not yet known how many people were in the building at the time and how many escaped.
Michael Paramasivan, who was in his seventh floor flat with girlfriend Hannah West, 23, and her daughter Thea, five, said: "If we'd listened to them and stayed in the flat we'd have perished".
People at the scene spoke of being unable to reach friends and family inside.
"I saw three people putting sheets together to climb down, but no one climbed down".
Nassima Boutrig, who lives opposite the building, said she was awakened by sirens and smoke so thick that it filled her home as well.
"I just saw a lot of people trapped, a lot of people screaming, children screaming".
N. Korea says it freed US student over humanitarian reasons
Warmbier was carried off the plane and taken to University of Cincinnati Medical Center. "Out of respect for the privacy of Mr. Warmbier and his family", said Tillerson, "we have no further comment". "We were just able to get the release of Mr Warmbier".
"We just need to know what is being used on apartment buildings, including those being retrofitted are fire retardant and meet Australian standards", he told Nine. It was fire up, up, up.
Assistant Fire Commissioner Dan Daly said:,"Firefighters wearing breathing apparatus are working extremely hard in very difficult conditions to tackle this fire".
Firefighters said they had rescued 65 people - some in pyjamas - from the 43-year-old block. My gut instinct told me just to get the girls out.
Witnesses described a white, polystyrene-type material falling like snow from the building as it burned.
"It is our conviction that a serious fire in a tower block or similar high density residential property is the most likely reason that those who wield power at the KCTMO will be found out and brought to justice!" a residents organization, the Grenfell Action Group, wrote in a blog post past year.
"I'm lucky to be alive. We also encourage residents to report any faulty fire doors or fire safety equipment immediately to the contact centre on 020 8356 3330 / 4440 so the Council can take action". "I'm standing here in everything I've got", one survivor said.
The building was recently upgraded at a cost of £8.6 million (NZ$15 million), with work to modernise the exterior finishing in May 2016.
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".
"It's too early to say or speculate but it certainly appears as though the fire has spread up the outside of the building, much more quickly than it should have done, something has gone wrong". "Hackney is once again at the forefront of resident safety with this fire sprinkler system, providing residents with an extra layer of safety in case the worst should happen".
The Citizen asked what Mayor Philip Glanville is doing to ensure that Hackney Council fulfils its obligations under the Regulatory Reform Act 2005 on Fire Safety with particular regard to high-rise blocks.
Comments