London Fire Brigade say "a number" of people have died at Grenfell Tower, after a blaze tore through the block.
Ambulances have taken more than 50 people to hospitals across the capital.
Police, firefighters and ambulance staff have been at the scene in west London since emergency calls started coming through in the middle of the night.
The first fire crews were at the tower within six minutes of the alert, London Fire Commissioner Dany Cotton has said.
She said she has never seen anything like the scene at Grenfell Tower and described it as "unprecedented".
One man described the "amazing firefighters" who were running into the building and up the stairs, as he was escaping.
"As I was going down the stairs, there were firefighters, truly amazing firefighters that were actually going upstairs, to the fire, trying to get as many people out the building as possible," he told the BBC.
People living in other buildings nearby have also been evacuated, because of the risk to safety.
London Fire Brigade assistant commissioner Dan Daly said: "Firefighters wearing breathing apparatus are working extremely hard in very difficult conditions to tackle this fire.
"This is a large and very serious incident and we have deployed numerous resources and specialist appliances."
"Our thoughts are with everyone affected," said Stuart Crichton, the assistant director of operations at London Ambulance Service.
"Over 100 of our medics are working hard to respond to this incident, including ambulance crews, advanced paramedics, advanced trauma teams from London's Air Ambulance and those staff managing the incident in our special operations centre."
"The emergency services in our country are world-class," said Emily Isaac on Newsbeat's Facebook page.
"If anyone is near these brave people, donate food and drinks to keep them going, do what ever you can to show them we are with them at this horribly hard time," said Sophie Jones.
Lauren Newbrook added: "These pictures made me swell with pride. Our emergency services guys are truly fantastic. I don't think I'd have it in me to do that job. Massive respect."