WATCH: Witnesses tell of screams and residents leaping from tower block

Others spoke of safety concerns and the panic sparkled by unfounded fears terrorism could be to blame for the disastrous fire.

One witness described hearing a neighbour screaming for help before apparently jumping out as flames engulfed his seventh-storey flat.

Speaking from an evacuation centre on Freston Road, the woman, who asked not to be named, told the Press Association: "We were being evacuated from Testerton Walk, which is next to Grenfell, at about 1am, at that point it looked like just one side of the building was on fire, but within about 40 minutes we could see at least three sides were burning.

"There was a woman stood behind me who was shouting to someone she knew on the seventh floor.

"She was on the phone trying to speak to him, she was obviously very emotional because the flats were blazing at this point.

"He looked like he was screaming to her.

"Police said for anyone at the windows to wave a rag or something so the firemen could rescue them, but we thought: how are they gonna do that?

"I saw the woman later and she was hysterical.

"She said her friend jumped.

"The whole of his window was on fire."

She added: "Everybody was crying. Nobody really knew what was going, or what is happening from now on.

"Where do people go? People have been saying the whole building could collapse at any stage. So frightening."

A long-time neighbour to the block, who saw the destruction unfold, said she at first feared terrorists were responsible.

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.

"I have lived here almost 21 years and I have never seen anything like this, at first I thought it was terrorism, we were just panicking."

A man who lived on the 17th floor of the block, identified as Methrob, told LBC Radio: "I heard the fire trucks and so I was alerted that something was going on.

"There was no fire alarm in the building, we don't have an integrated fire alarm system.

"I went outside my house and I could smell the smoke.

"I looked out my window, I leaned over and I could see the fire blazing up.

"I woke up my auntie who was sleeping, it was about 1.15am, and we started to make our way down.

"I warned a couple of my neighbours, the ones nearest to me, and we basically went as fast as we could."

He said the fire was inside one apartment, but added the "real issue was when it caught fire to the cladding outside.

"That's when I noticed the fire from outside when I looked out the window.

"By the time that we got downstairs, the fire had gone all the way up and it was just about reaching our windows on the 17th floor.

"The whole one side of the building was on fire.

"The cladding went up like a matchstick."

Methrob said residents had been concerned about safety, adding there had been warnings "for over a year".

He said one man was "trying to get everyone to get together to do something before it was too late".

Another witness, Samira, told BBC News: "It escalated really quickly.

"Around midnight the fire was only around the third floor and then, before you know it, the whole 23 (sic) floors of the building were all on fire and there were people screaming for help and throwing kids out.

"I think everyone felt really helpless because no-one could get to them.

"Everyone was really scared and they didn't know what to do and it was really sad to see.

"These are all people that we grew up with and people that we see every day, like our neighbours.

"There was a lot of people there, children, elderly people and disabled people; my family members, who thankfully made it out.

"But there are still a lot of people who are unaccounted for."

Joanna O'Connor, a local resident, told Sky News: "At about 2am woken up by screaming, sirens and helicopters.

"We came outside and were confronted with the building that was completely engulfed in flames.

"It was a real shock and there were hundreds of people lining the streets, we could still hear screaming from the building and people were milling around in shock crying.

"One of our neighbours, her sister, husband and children were in the building, it was their neighbours' flat that caught fire.

"So it's very close to us, we've got neighbours whose families are in that building."

Local resident Tamara told BBC News: "Around 12.30/1am my mum called me and said there was a fire outside.

"By the time I got there the whole right side of the building was on fire, the whole thing was engulfed in flames.

"We could hear people screaming 'help me' so me and my brother, with some other people who live in the area, ran over to the estate to where you could still get underneath it and there were people just throwing their kids out saying 'save my children'.

"The fire crew, ambulance and police couldn't do anything, they couldn't get in, and they were just telling them to stay where they are, and we'll come and get you.

"But things quickly escalated beyond measure and they couldn't go back in and get them.

"Within another 15 minutes the whole thing was up in flames and there were still people at their windows shouting 'help me'.

"You could see the fire going into their houses and engulfing the last room that they were in."

Tamara went on: "My brother has a lot of school friends who are still wondering if their friends have made it out, they haven't got in contact with them or heard anything.

"One of the girls lives on the top floor, which the police advised that if you were living on that floor that it is most likely that they haven't made it."

Samira added: "I think the speed of the fire was the most shocking thing for everyone, how quick it literally went from zero to 100.

"Like it was literally just the fourth floor and that was bad but it was really minor, and that building is really big and the whole building was gone, even before it hit 1am the whole building was in flames.

"I saw people flying out of their balconies and windows.

"I saw a man who flew out of his window, I saw people screaming for help.

"We saw a lot of people jumping out that basically didn't make it.

"It was from the eighth floor and up, and that kind of floor you wouldn't really make it."

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'.

"I was watching TV in bed and I could smell smoke and then I heard a fire engine and I jumped up.

"I went to my back bedroom, I thought if something was on fire I would see, and I was just speechless, the guy next door was screaming at people to get out of the building.

"Then about 20 minutes later when I went out the front I could see all the debris coming down and I could see the crap coming down and a police officer told me to shut the door and leave and go to the end of the road.

"It was like something out of a nightmare."

Singer Cerys Matthews, who lives nearby, said she was woken by a helicopter.

The Catatonia star told BBC Radio 5 live: "When we saw it in the early hours of the morning, the fire caught on the fourth floor.

"The flames ripped up the side of the building along this cladding which clads every single side of the building."

She went on: "It's unbelievable that we're watching this in 2017.

"What we're hearing is that nobody heard any alarms; that there was one exit and this is a 24-storey building. Young families, they were advised the stay put if a fire was going to break out.

"The most chilling thing is that the residents have had an action group for many years."

She said: "We're a tight community - people from all over the world living here.

"People are just so shaken. It's devastating. This is 2017. How can we not have had these high-density buildings safeguarded for this kind of major, major incident?

"This is London, This is the UK. This is the first world.

"The residents have been crying out for years, saying this is not safe. How can we have accepted that?"

A panicked parent was seen throwing her children from a window in the block shortly after 2am, one witness said.

Joe Walsh, 58, said: "I saw the parent throw two kids out of the window.

"I don't know where they landed because I was on the other side.

"I doubt anyone caught them, I hope they did.

"It wasn't that high up - it would have been the fifth or sixth floor up. There were still people screaming at quarter to four this morning."

Mr Walsh has thrown open the doors of his Maxilla Social Club as a refuge for displaced families.

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WATCH: Multiple fatalities as fire engulfs tower block trapping residents in flames