Murder squad detectives are urgently trying to find Miss Blake's boyfriend Arthur Simpson-Kent following the discovery.
Her body, along with sons, Zachary, eight, and Amon, four, were found in the garden of the family home in Erith, Kent, earlier this week.
During a press conference at Scotland Yard Miss Blake's sister Ava said: "We've got to use our faith to get us through this.
"I want him back to justice because I want to know why and what happened."
Simpson-Kent is thought to have fled to Ghana in west Africa after being interviewed by police about the disappearance of the mum of two.
A Scotland Yard spokesman said: "Whether or not he is in the country is one line of inquiry."
Miss Blake broke down in tears as she paid tribute to her sister.
"I have lost my sister and my nephews. I'm not going to see them grow up," she said.
"I'm going to miss Sian. She was my sister and someone I loved. I was proud of her as an actress. I just wanted the best for her and my nephews.
"We always had hope because of certain things we were told by police. That hope was always there."
Previously an unknown actress, Sian Blake's big break came when she was introduced as soul singer Frankie in EastEnders in June 1996 by series producer Jane Harris.
She was in the BBC soap for 56 episodes, reportedly quitting because of hostility from viewers towards her manipulative character.
The performer, who later worked as a sign language tutor, also appeared in episodes of The Bill, Casualty, Doctors and Skins, and was the voice of Yugiri in 2015 video game Final Fantasy XIV: Heavensward.
