Scotland Yard named the victims as Lorna and Connie Morrison, 34 and 27, and their mother's partner, Noel Patterson, 62. All three were tied up and killed in the same room. The sisters' mother, Evelyn Daley, was at work on Thursday night when the killings are believed to have taken place.
A friend arrived at the flat to find the front door open and the victims lying in a pool of blood on the living room floor. One police source described the scene as "carnage". Lorna Morrison's nine-month-old son, Christiano, was also in the flat. The attackers seem to have chosen to let the child live.
Detective Superintendent Gary Richardson said: "It would appear that the victims had been incapacitated by the use of restraints." Police say that they want to speak to three youths seen entering the block of flats on the Stonebridge estate close to the time the victims were shot.
Mr Richardson said that detectives were keeping an open mind about the motives. He said: "That is one of our main lines of inquiry, to find out why these people were targeted if indeed they were targeted." Officers were not ruling out the possibility that the killings could have been the result of a burglary.
Neelam Hussain, a neighbour, is reported to have said: "There was a knock at my door. There were three black men there and they said they were looking for someone. I said 'there is only me here'. So I shut the door. A few minutes later I heard gunshots. I used to see the mother pushing the baby. She would be smoking a joint at the same time."
Operation Trident, which deals with gun crime among London's black communities, is investigating the incident. Trident, founded in 1988, has traditionally focused on drug-related shootings. The Stonebridge estate became notorious in the 1990s because of crime and drugs. A seven-year-old and her guardian, a crack dealer, were shot dead there in September last year.
Residents of the estate described the elderly victim, Noel Patterson, as a hard-working and friendly man. A neighbour said: "I saw him every day working long hours as a cleaner. He strived at his job but was always smiling. He was a kind, simple man and I can't understand why anyone would want to kill him."