Police believe at least one person was living on and off at Sarah Gatt's Kensington flat while her body lay decomposing in the bathtub for nearly nine months.
No-one knew the mother-of-four had been killed last April until police found her remains in January.
Ms Gatt, 40, died after a violent assault, but her killers deliberately tried to make people think she was still alive, police said.
"That Sarah was somewhere else, or there's an explanation as to why she hasn't been seen for a period of time. The information we have is that these types of stories have been relayed multiple times to multiple people," Detective Inspector Tim Day told reporters.
Ms Gatt's body was discovered in January when police visited the housing commission flat and detected a foul smell.
That's when they made the shocking discovery of the body decomposing in the bathtub.
"No-one deserved to die like that," Ms Gatt's stepmother, Cheryl Gatt, said. "It doesn't matter what happened or what her life was."
Her family describe her as an ambitious woman, who had dreamt of being a model as a teenager.
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In recent times, however, drug use had dominated her life and her parents and sisters lost contact with her around 18 months ago.
"I put her in different places to try and get her cleaned up but it didn't happen," her father, Victor Gatt, said.
Three men and two women have been interviewed over Ms Gatt's death and released without charge.
Detectives particularly want to speak with any witnesses who saw people coming or going from the property after April 20 last year.
"Please come forward," Cheryl Gatt said. "She deserves that."