At least 125 firefighters and 20 fire engines were called to the scene and firefighters were still seen dampening down the block on Elm Road on Tuesday morning.
The London Fire Brigade said that initial investigations confirmed that cladding was involved in the blaze.
Hundreds of Petworth Court residents were evacuated, with some recounting the “frightening” moment they were told the leave - which reminded some of the Grenfell Tower fire.
Mar, a mother of one who lives on the fourth floor, told the Evening Standard that residents wanted to see “a full investigation”.
“The cladding on this building was down to be replaced two years ago but nothing has been done,” she told the paper.
“It’s scary and devastating to think that we still have cladding that everyone knew could be dangerous. This could have been another Grenfell, we are very angry and want a full investigation and answers.
“They had put in some fire measures inside the building to make it safer but what’s the point if the cladding is still in place?”
The aftermath of the Grenfell Tower fire - which left 72 dead in 2017 - has seen calls for the removal of flammable cladding from buildings.
Brent North MP Barry Gardiner told the Standard that he had “repeatedly warned” the block’s managers about the safety risks the cladding imposed.
Resident Amare Gealam, 28, also told the Evening Standard: “It was very frightening. There were police and firefighters knocking on the doors. The fire started small then went up quick.
“I don’t know whether that’s because of the cladding but you couldn’t help thinking of Grenfell.”
The Fire Brigades Union issued a warning over the use of cladding after over 100 firefighters were called to put out the fire.
“Firefighters have once again been called to cladding fire which could have resulted in tragedy,” Matt Wrack, Fire Brigades Union general secretary, said.
“Decades of deregulation have created unnecessary risks to residents and firefighters, and put homes and lives at risk.”
The London Fire Brigade said that half of the external side of the building and all of the roof and four external balconies were damaged by the fire.
Five adjoining blocks were also evacuated as a precaution. All residents were accounted for following the evacuation and there were no reports of any injuries.
The Independent has contacted Octavia Housing for a comment.
A spokesperson told the Standard that staff had been on site and confirmed the building has external cladding.
“The building has some external cladding in its construction, and we are working with the developer and our insurer to get this removed. There is a plan in place to address this which includes on-going negotiations with the developer and our insurer as part of an arbitration process,” a spokesperson told the paper.
They added: “The safety of residents is paramount and the needs of those with vulnerabilities have been prioritised.
“Our emergency planning procedures were activated. We ensured all evacuated residents were supported with access to welfare facilities. Overnight hotel accommodation was found, where required, for residents who were unable to return home and they continue to be supported.
“The London Fire Brigade is on site this morning and we are awaiting an update from them. The fire brigade have yet to determine the extent of the damage and cause of the fire.
“Petworth Court has a Fire Risk Assessment which has been shared with the London Fire Brigade, who we have been working with since last August to manage the building.”