Jody Martin said he got to the scene as the first fire engine was arriving at Grenfell Tower.
He told the BBC: “I grabbed an axe from the fire truck, it looked like there was a bit of confusion about what to do.
“I ran around the building looking for a fire escape and couldn’t see any noticeable fire escapes around the building. A lot of debris falling down.
“I eventually gained entry onto the second floor, and once I got to the corridor I realised there was so much smoke there.”
He added that given the thickness of the smoke, he would be surprised if anyone could have left the building without assistance.
“I watched one person falling out, I watched another woman holding her baby out the window … hearing screams, I was yelling everyone to get down and they were saying, ‘We can’t leave our apartments, the smoke is too bad on the corridors’,” he said.
Two hundred firefighters and 40 fire engines are battling a large fire on a west London estate.
At least two people have been injured and flats at the 27-storey Grenfell Tower are being evacuated.
Footage on social media showed the building engulfed in fire, with flames stretching over a number of floors.
The fire brigade said the fire had spread throughout the entire building.
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.”
Reporting from the scene, Sky News producer Dan Cairns, said residents have been told that, if they get calls for help from people inside, to tell them they need to try and “self-evacuate”.
He added: “They are being told to put a cloth over their mouths and try to get out by themselves.”
London Ambulance said it had sent a “number of resources” to the scene, including its Hazardous Area Response Team.
London mayor Sadiq Khan tweeted: “Major incident declared at Grenfell Tower in Kensington” and urged people to follow London Fire Brigade on Twitter.
One witness, Reo, told Sky News: “I was in my kitchen and heard smoke alarms.
“I could see the whole right side of the building was on fire.”
Celeste Thomas lives across the road from the tower and said residents and families were “trying to find each other” following the evacuation.
She said: “Police have moved everyone back out of direct sight but I can hear cracking and debris falling.”
The tower block is on the Lancaster West Estate, between Latimer Road Underground station and Westfield’s White City shopping centre.
Police said: “At this stage we are aware of two people being treated at the scene for smoke inhalation.”
Transport for London said there was no service between Hammersmith and Edgware Road on the Circle and Hammersmith and City lines, while the police said the A40 was closed in both directions, owing to the fire.