Five London hospitals have received patients affected by the blaze that engulfed a tower block in west London.
NHS England said no details were available at present on the condition of people taken to hospital.
The five hospitals are St Mary's, Chelsea and Westminster, Royal Free, St Thomas' and King's College Hospital.
A spokeswoman for NHS England London region said: "Our thoughts are with everyone affected by the tragic incident at the Grenfell tower block in Kensington.
"Our priority is to continue to work closely with the NHS and emergency services involved. We have tried-and-tested measures in place to manage this but we would also encourage Londoners to use NHS services wisely and seek advice from NHS 111 in the first instance."
London Ambulance Service said it had taken more than 50 people to the five hospitals.
More than 100 medics from the service responded to the incident.
Multiple deaths as 'unprecedented' blaze engulfs tower block
Several people have died after a huge fire destroyed a tower block in west London with witnesses reporting residents trapped on upper floors as the flames tore rapidly up the building.
People who escaped the 24-storey Grenfell Tower in north Kensington spoke of others, including children, screaming for help, some holding babies from windows and others jumping from their flats high above the ground.
London Fire Commissioner Dany Cotton said there had been a "number of fatalities" but could not say how many due to the size and complexity of the building.
She told reporters: "This is an unprecedented incident.
"In my 29 years of being a firefighter, I have never ever seen anything of this scale."
She said firefighters had only managed to get to the 19th and 20th storeys of the building.
Residents who escaped the inferno complained there had been no fire alarm, with people relying on neighbours to wake them as the blaze spread.
They said official advice in the event of a fire had been to stay inside.
Mickey Paramasivan, who was in his seventh floor flat with his partner and child, said: "If we'd listened to them and stayed in the flat we'd have perished."
London Fire Brigade said the cause of the fire was still being investigated.
But several residents reported one man had said it started in his faulty fridge.
Samira Lamrani, 38, said: "He was just beside himself.
"He was just as surprised at how quickly the fire spread as anybody else.
"I could hear him saying that he contacted the emergency services immediately and they reassured him everything would be under control within a short period of time, and obviously it wasn't."
Residents said refurbishment work had recently been carried out, with cladding on the outside of the structure and work on the gas supply.
A residents action group said its warnings about safety had fallen on "deaf ears".
A blog post from the Grenfell Action Group in November 2016 said "only a catastrophic event" would expose the concerns residents had.
The group said there was one entry and exit to Grenfell Tower during improvement works and it had issues with evacuation procedures.
Following the fire, the group posted: "All our warnings fell on deaf ears and we predicted that a catastrophe like this was inevitable and just a matter of time."
London mayor Sadiq Khan said in a statement: "There will be a great many questions over the coming days as to the cause of this tragedy and I want to reassure Londoners that we will get all the answers."
Pictures from the scene showed flames engulfing the block and a plume of smoke visible across the capital, while others showed residents looking out of windows in the block.
The leader of Kensington and Chelsea Borough Nick Paget-Brown said "several hundred" people would have been in the block when the fire broke out.
Witnesses said the fire spread rapidly up the building, with some suggesting it was fuelled by gas.
Muna Ali, 45, said: "The flames, I have never seen anything like it, it just reminded me of 9/11.
"The fire started on the upper floors ... oh my goodness, it spread so quickly, it had completely spread within half an hour.
"My friends live on the fourth floor, someone knocked on their door, they didn't know and they got out. They have three children.
"Some people were knocking on doors but the people inside didn't open the door."
Ann Waters lives in a house at the foot of the tower and was forced to flee her home when burning debris began raining down.
The 57-year-old said: "It was the screaming that was the worst and I could hear that from the ground. All I could hear was 'help, help, help'."
She added: "It was like something out of a nightmare."
Mr Paramasivan, who was woken by the smell of burning at around 1.30am, said: "I looked out into the corridor and saw there was smoke everywhere and neighbours running around and a fireman saying get down the stairs.
"I went inside, grabbed my little girl and my girlfriend, and ran.
"Our advice has always been if there is a fire stay in your flat, but if we had stayed in that flat we would have been perished. It just spread like wildfire, and the smoke alarm was useless, We would not have heard anything.
"It was like something out of a disaster movie."
He added: "I did see people working on a stairwell with a gas pipe over the past few weeks.
"There was a lot of blue flames (in the fire) which made me think it was gas related and I think it was the plastic cladding that made it spread so fast."
Actor and writer Tim Downie, who lives around 600 metres from the scene in Latimer Road, said: "It's horrendous.
"The whole building is engulfed in flames.
"It's gone. It's just a matter of time before this building collapses."
Jody Martin said he got to the scene just as the first fire engine was arriving.
He told the BBC: "I watched one person falling out, I watched another woman holding her baby out the window... hearing screams, I was yelling everyone to get down and they were saying 'We can't leave our apartments, the smoke is too bad on the corridors'."
Fabio Bebber wrote on Twitter: "More screams for help as the fire spreads to another side of the building.
"We can see how quick the fire spreads via the external panels. It's unbearable hearing someone screaming for their lives at #grenfelltower."
George Clarke, who presents the Channel 4 TV show Amazing Spaces, told Radio 5 Live: "I'm 100 metres away and I'm absolutely covered in ash.
"It's so heartbreaking. I've seen someone flashing their torches at the top level and they obviously can't get out."
Paul Littlejohn said: "Windows were smashing and exploding, people jumping out and trying to climb out with rope made of out of bed sheets.
"It was a complete nightmare.
"You'd think after millions of pounds was spent on the tower block that it would be safe and this event could not happen."
London Ambulance Service said paramedics had taken more than 50 patients to five hospitals.
More than 200 firefighters were sent to tackle the blaze which was reported just before 1am on Wednesday.
Firefighters were on the scene within six minutes.
An acrid column of smoke could be seen rising from the building on Wednesday.
The charred structure still had pockets of flame rising from several storeys as desperate efforts to bring the blaze under control continued.
The Metropolitan Police have set up a casualty bureau for anyone concerned about their friends and family on 0800 0961 233.
Matt Wrack, general secretary of the Fire Brigades Union, said: "Lives have been lost, many people have suffered serious injuries and others will be made homeless as a result of the fire.
"...A full investigation will need to be undertaken at the first possible opportunity to establish exactly what happened and what can be done to prevent such an incident happening again."
Denise Bloomfield, 37, who was evacuated from a nearby flat, said: "You could feel the heat from where you were standing. It was scary. It was like watching a movie.
"People were like zombies in their pyjamas. It was just not real."
She had looked out of her window and "saw the whole building on fire and people screaming for help".
She said: "We ran out and saw the whole building on fire. People near me were screaming because their loved ones were there.
"There was nothing you could do because we were being pushed back. There was nothing you could do because it was too big. The fire just took so quickly.
"There were people who were just surviving ... and waiting for the fire to take them, just waiting to die.
"They were taking in air from the window. One person had a light so you knew they were there."
Copyright (c) Press Association Ltd. 2017, All Rights Reserved. Picture (c) Jonathan Brady / PA Wire.