Flora Neda, who lived on the 23rd floor of the building, claimed residents said they were told to go to the top floor and wait for rescue by helicopter as the fire raged.
The 55-year-old told Channel 4 News: “35 or 40 people came up and they said the fire brigade told us you have to go up and we send for you helicopter rescue.”
She added: “One of the Iranian ladies (who took refuge in her flat) spoke to her (own) son who said that he wanted to come take her away.
“She replied that this was not necessary as the helicopter was coming to take them away.”
Mrs Neda’s son, Farhad, 24, does not believe residents were told they would be rescued on the top floor.
He told the programme: “I don’t think anyone was instructed to seek help from the helicopters.
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“There were helicopters up. I’m not sure how many. There was definitely more than one.”
The London Fire Brigade also denied they they instructed residents to head to the top floor.
A spokeswoman said: “Grenfell fire was an unprecedented fire and due to the ongoing investigation we cannot go into details about what happened on the night.
“That said we can confirm that we do not use helicopters to conduct rescues from high rise tower fires.”
Mrs Neda arrived home with her son and husband Saber, 57, just 30 minutes before the fire started.
Mechanical engineering graduate Farhad said they were told firefighters were on their way up and to stay in their flats – before worried neighbours banged on doors to tell people to get out.
He said that when fire broke the windows of their flat and had come into the bedroom, his mother threatened to jump out of the tower, and told him: “I don’t want to burn. I don’t want to go through the pain of burning alive. I’m going to jump out the window.”
He said: “So I just grabbed my mum, so that she didn’t jump out the window, I pulled her. And I said ‘OK we need to at least try to get out’. We thought we were dead 100% that night. So I said ‘at least let’s try’.
“And at that point I grabbed my mum, and because there was so much smoke I didn’t let go of her. Because I knew that if I let go I wouldn’t be able to find her again. So I took her and we started feeling our way.
“She suffers from myasthenia gravis, which is a muscular condition. So I knew it would be difficult for her to go down stairs especially.
“So I was carrying her weight above on my shoulders and we just made our way out. And we literally couldn’t see anything. It was so difficult.”
Flora told Channel 4 News how she tried to persuade her husband to leave with them, saying: “I called to him so many times to keep away from the window. He was standing and watching the fire. And then my son took my hand and said ‘Mum you have to leave here’. I called my husband and said ‘let’s go’. He said ‘I’m behind you’.”
Mr Farhad ran down a stairwell through thick smoke, with his mother on his shoulders, and said: “We were stepping over people and she was asking me ‘what are we stepping on?’ and I didn’t want to scare her so I said ‘It’s just the fire brigade’s hoses that we’re stepping on.’”
The pair were then helped by firefighters, and were put into an induced coma in hospital.
Mr Farhad said he believes his father, who jumped from the building, stayed behind to help other neighbours.
He said: “I think he was trying to help the other neighbours who had come into our flat – the four ladies – to help them get out as well.
“He was always the type of person who would try to help other people before himself. I know that he wouldn’t have left anyone in there.”
The extraordinary story from inside the fire comes on the day that the public inquiry into the causes of the tragedy begins.
Chairman Sir Martin Moore-Bick, the retired judge chosen by Prime Minister Theresa May to lead the inquiry, will give his opening address at the Grand Connaught Rooms in central London.
The former Court of Appeal judge will not take questions following the hearing, which is expected to last around 45 minutes.
Survivors and victims’ families will be able to watch live on a screen in Notting Hill Methodist Church, where they are likely to be listening intently to the language and tone of Sir Martin’s opening.
The chairman faced anger from the community in a series of public meetings designed to help shape the terms of reference but, once these were announced, the inquiry was criticised for excluding an examination of wider social housing policy.
Campaigners had pressed for the probe to scrutinise the systemic issues underlying the cause of the tragedy on June 14, when at least 80 people died.