Three children are among the fatalities following the blaze in Channel Close last on Sunday evening.
A seventh man was taken to hospital with serious burns and is still receiving treatment; his condition is not thought to be life-threatening.
The Met’s senior investigating officer Detective Chief Inspector Garth Hall said: “Firstly, I want to express my sincere condolences to all those affected by this terrible incident. The deaths of so many people, including children, is simply heart-breaking.
“We intend to complete a meticulous investigation into how this tragedy happened. For many days now the scene has been too unstable and dangerous to complete many of our inquiries. It was only after the walls were shored up, and the roof removed, that it became safe enough for search teams to enter the premises.
“We have now been able to sadly confirm the death of a sixth person. The investigation into the cause of the fire continues and I must express my thanks to the London Fire Brigade, their knowledge and experience has been crucial in helping us understand what may have happened that dreadful night.
“These deaths are still being treated as unexplained and we are liaising closely with the Coroner. We understand that family and communities will be looking for answers, but this will be a thorough investigation and we will not rush to any judgement, but follow where the evidence leads. Should there be any change in the nature of this inquiry, we will share that information immediately.
“Lastly, we are still appealing for witnesses, or anyone who recorded anything on their phones that night, to come forward. If you have anything that can assist this investigation please get in contact. Any bit of information, no matter how small, may help us understand what happened that night.”
Any witnesses or anyone with any information is asked to call police on 101 or contact via X (Twitter) @MetCC. Please quote Operation Hamalton. To give information anonymously contact Crimestoppers on 0800 555 111.