Eight fire engines and 60 crew were sent to tackle the blaze on Deacon Street in south London.
Residents were evacuated across three floors of the building due to intense smoke, according to the London Fire Brigade.
Flames were seen shooting up from an apartment balcony shortly before 11am and the fire was under control by 12.15.
Fire investigators have started trawling for clues as to how the blaze started.
Station Commander Dave Hill, who was at the scene, said no injuries have been reported.
“Firefighters worked incredibly hard to bring the fire in Elephant and Castle under control,” he added.
Valeria Monterosso, 22, who lives in the block of flats, said she was at her friend’s home nearby when the fire began.
She said: “I heard ambulances and went outside because I thought I should check on my dog, Marcello.
“I walked over and saw about 15 trucks and thought, ‘oh my God’.
“I saw smoke coming out of the building and was just concerned if everyone was OK. I’ve asked and they’ve (the emergency services) told me everyone is fine.
“My dog is still inside and I’m worried about him, but the police have told me it’s going to be a few hours until they let us back in.”
— Liam Jack (@liamdmjack) November 4, 2021
“The Brigade’s drone team assisted by providing an aerial view of the incident.
“Road closures are in place and there is heavy congestion. Firefighters are expected to remain on scene this afternoon and we encourage people to avoid the area.”
— London Fire Brigade (@LondonFire) November 4, 2021
“Road closures are in place and there is heavy congestion. We encourage people to avoid the area.”
Londoners shared their concerns on Twitter as smoke from the fire billowed across south London.
“Yikes. Avoid Elephant and Castle. Flat fire so no access to roads around the Walworth Road,” one person said.
Another commented: “Elephant and castle in disarray. New build on fire, LFB Southwark attending. Hoping everyone is okay.”
Fire crews from Lambeth, Dockhead, Dowgate, Brixton and surrounding fire stations were sent to the scene.
London Fire Brigade said while the building had cladding, it was not ACM cladding – which was used on Grenfell Tower – and was not affected by the fire.
A spokesperson for Lendlease, the developer for Hurlock Heights, said: “A flat fire at Hurlock Heights has been extinguished and our thanks go to the emergency services for their swift response. A full and comprehensive investigation will be carried out into the cause of the fire.”