Firefighter Martin Gillam told the public inquiry how his team had rescued a woman trapped near the top of Grenfell Tower.
He and his colleagues were instructed to go up to the roof to help fight the fire from above, but soon realised they would not have enough oxygen to complete the task.
On their way up they passed firefighters who said they had been unable to rescue a woman on the 20th floor.
Mr Gillam and his crewmates, who were wearing extended breathing apparatus giving them more time under oxygen, decided to try and reach her.
They found the woman lying "coughing and spluttering" in the stairwell between the 20th and 21st floors.
After giving her some oxygen, the group attempted to guide her to safety.
In a written statement to the public inquiry, Mr Gillam said: "The journey down the stairs started off quite well, she was fully with it, really co-operative, keen to get out but she was switched on.
"We started walking and we must have been on 17 or 18 and it's started getting hot and she started screaming.
"She probably screamed for maybe a floor, floor-and-a-half, and then she just went. She collapsed unconscious behind us on the floor."
Mr Gillam went on: "My whole head, my neck and ears was just burning.
"I remember saying to whoever was behind me 'are you burning?' and he said 'yeah I'm burning' so I said 'we need to get out of here'.
"There wasn't much visibility at all. We are probably on like (floor) 11 now. We are basically just going down through a chimney.
"I keep myself fit all the times, but I had nothing - I was completely gone.
"I said to Deano (a fellow firefighter) 'you're going to have to take her or I'm going to drop her'. She has thrown up at this point and she was gone, she was out of consciousness."
Mr Gillam said he brought the woman out of the tower to the ambulance service, and later checked up on her.
He said: "She recognised me straight away and she said 'thank you thank you'.
"We gave each other a hug. I said 'you're out now, you're fine' and she said 'thank you thank you'.
"It was really quick. I just wanted to make sure she was alive.
"In this job you get people out of cars, trains or whatever and you never see them again."