A fire broke out in a high-rise flat a short distance from the site of the Grenfell Tower disaster.
Ten fire engines and 70 firefighters were sent to the scene in Darfield Way, the London Fire Brigade said.
The fire on the 12th floor of Markland House was brought under control by 12:55 BST and no injuries have been reported. Its cause is not yet known.
The block of flats is under a mile from Grenfell Tower where seventy-two people died on 14 June 2017.
Resident Dhin Chittenden said she cried as she ran down the steps from her flat on the 11th floor of the tower block.
The 26-year-old receptionist, who has lived in the building with her husband for a month, said she was already fearful about another Grenfell Tower-type tragedy before the fire broke out.
"I kept thinking about that. If it's happened somewhere else then it could happen again," she said.
Billy Hunt, who had been sleeping after a night shift but was woken by the smell, said he did not feel safe living in the tower block.
Mr Hunt, who knocked on neighbours' doors on his way out to alert them to the blaze, said he heard no alarms, adding: "They should be going off all over the place, especially after Grenfell."
The 57-year-old, who has lived in Markland House for 27 years, said someone told him the fire hose had only reached the fifth floor, and called that "ridiculous".
Samantha Findley, 41, smelled what she thought was burning plastic in the tower block before immediately fleeing her 10th floor flat.
"I smelled it. So I thought 'let me get out, I'm out'. I grabbed my keys, my phone. I'm out. I'm not seeing where it is or anything. I'm out."
Miguel Alves, who survived the Grenfell Tower blaze in 2017, was passing the area when he saw fire engines and police.
He said: "I feel shocked because it's only 200 metres or 300 or 400 metres anyway from Grenfell Tower. It's on the same area. It's difficult to believe something happened again on the same area."
London Ambulance Service urged people living near the scene of the fire to keep their windows shut.
A cordon is in place around the tower and a roll-call of residents was taken to ensure everyone was out of the building.
London Fire Brigade policy states: "If the fire isn't in your own flat and your flat is not affected by smoke from a fire elsewhere in the building, it's often safer to stay put."
Updated 7th October 2019: This article has been updated to refer to the London Fire Brigade's policy for escape from flats during a fire.