"I heard shouting, 'It's getting bigger, it's getting bigger!'," he told CNN Wednesday.
By the time he had grabbed his daughter and ran down the stairs, Paramasivan said half the building was on fire and the other half was catching fast.
"If I'd fallen asleep, we would have all been dead ... There weren't no warning, there weren't no proper noise to let us know what was happening. We lost everything. Everything in the house is gone," he said.
Many residents who evacuated said the fire had spread incredibly quickly with almost no warning.
Some people told CNN they didn't even hear a fire alarm.
Khalid Ahmed, a 20-year-old student who lived on the eighth floor, was playing video games when he smelled smoke. As he walked to his kitchen to investigate, he saw "sparks coming up" from the window.
Ahmed woke his aunt and started knocking on his neighbors' doors. "One of my neighbors ... came to his door, looking confused, and asked what was wrong. When he stepped out there was suddenly smoke everywhere, the whole corridor was engulfed. Everyone started coughing and couldn't breathe."
Ahmed and his neighbors escaped to safety through the only communal stairwell for the whole building. "I watched flames burst out of our window and our flat was engulfed in flames," he said.
On Friday, Ahmed had noticed a white powdery substance on the floor in his corridor. He thought that maintenance workers were possibly trying to cover exposed red pipe, believed to be gas pipes, on the eighth floor.
Neighbors woke to screams
Matt Kane, who lives in the building next to the Grenfell Tower, said he was woken by screams and sounds of people running.
"I got dressed, went downstairs and saw a neighbor. She said 'fire' and I thought it was the school across the road. I walked out and saw the tower on fire," he said.
One local man, David Phippen, said he was woken by residents of Grenfell shouting for help, and saw the lights were still on in one side of the building while the other side was in flames.
"I thought there was a row going on," he told CNN. "I came out to my back garden and saw (the fire). You could hear people screaming. Whoever is at the top of (the tower), I pray to god they got out."
Some said the speed of the fire made them nervous about the state of their own buildings. Ubah Yusuf said she and her neighbors, who lived close to Grenfell, would ask their building manager about their own tower block.
"The fire started from the bottom, people on upper floors couldn't get out. I'm worried about my building now," she said. "I'm worried if a fire happens, who is going to help?"
Residents jumped from windows
Numerous witnesses also described seeing people trapped inside their apartments; banging on windows, shining lasers and lights or calling for help.
Two women who watched the fire break out said they saw multiple people jump from the top floors of the tower to try to escape.
Samira Awil said she had seen multiple bodies, including children, covered in sheets outside Grenfell Tower where they had fallen. "Luckily for me, my little brothers and sister were safe in their beds, but people their age (were) dying," she said.
"We literally watched a man burn to death in his flat," her friend, Tamara Eastmond said. "We saw the flame enter his flat and (overcome) him."
Another witness, Abdullah Barraq Mohidin, said the fire began as a small one "but no one left their houses."
"I can't believe that no one went inside to help them," he said. "There was people trying to break their windows ... a woman and a child waiting for people to help them for three hours. Three hours there shouting for help."
A baby was 'miraculously' saved
Samira Lamrani, who lives next to the Grenfell Tower, told the Press Association that she watched a woman throw her baby from a window.
"A woman was gesturing that she was about to throw her baby and if somebody could catch her baby," Lamrani said. The baby was "miraculously" caught by a member of the public, however is not clear what happened to the mother, she said.
"Endless numbers of people" remained trapped inside and were screaming for help at the windows, Lamrani added.
"Us members of the public were reassuring them, telling them we've done what we can... but obviously the look on their face was death.
"I could hear them screaming for their lives," she said.
Friends, relations caught in blaze
Ahmed Chellat, who lives opposite the Grenfell Tower, is anxiously awaiting news from his brother, who lived on the 21st floor of the complex along with his wife and their three children.
Chellat told CNN he last spoke with his sister-in-law by phone around 2:20 a.m. During the call, she said that emergency services had arrived and had instructed the family to remain inside their smoke filled house.
"'They are coming to get us,'" she told Chellat.
But more than 12 hours later, Chellat still doesn't know where his family is, and is calling on authorities to provide him with any information.
"If you saved them, let us know where they are," Chellat said. "I'm hoping for the better, because its a whole family that would be wiped out."
Local resident Ness Davis said a close friend of hers had been trapped inside in the building. "(When I called) all she said is, 'It's hot, it's hot, it's hot," she told CNN.
When Davis attempted to contact her friend later on, she didn't answer the phone.
Tales of heroism were already beginning to emerge Wednesday morning. Ayyub Asif told CNN his family lived on the 18th floor and as soon as he saw the flames from his own house, miles away, he ran toward the blaze.
Police wouldn't let him through when he arrived but eventually he made his way inside.
"We brought them out and we held them in our arms, and the paramedics brought them to the hospital," Asif said. "You can't get away from a fire on the 18th floor, but God's grace, they got away."
"Seeing your little cousin in your hands and not breathing properly, it's a mad thing," he said.