Three people were rescued by firefighters after they were called to a property on Russett Way just before 6am on Saturday.
A five-year-old boy was taken to hospital and died on the same day. A post-mortem examination gave his cause of death as inhalation of fire fumes.
A 14-year-old boy and a 34-year-old woman have now also died of their injuries, the Met said on Thursday.
All three were members of the same family and their relatives have been informed. They are being supported by specialist officers.
Detectives from the Met’s Specialist Crime Command believe the fire was started deliberately, but they are not looking for anybody else in relation to the investigation.
Detective Chief Inspector Laurence Smith, said: “This was a truly awful incident and we are doing everything we can to support the family’s next of kin.
“We have been working alongside specialist investigators to establish the cause of the fire and it saddens me to say that we believe it was started deliberately, inside the address, by one of those inside.
“While I accept we may never know the circumstances, I am still very keen to hear from anybody who has information that could shed any light of this tragic incident.”
If you have any information that can help please call the incident room on 0208 345 3985, with the reference Operation Tampere.
You can also tweet @MetCC or call 101 quoting 1231/06Mar. To give information anonymously contact the indepdent charity Crimestoppers on 0800 555 111.
