Police released a grainy photo of Saldanha on Saturday. A native of India, she had lived in Bristol in southwestern England with her family for the past nine years, Scotland Yard confirmed.
Police said her death is being treated as "unexplained," though they said they didn't find anything suspicious. A coroner will make a determination on the cause next week.
Flowers were left outside the hospital's nurses' building. Attached to the red, white and blue flowers, a note read: "Dear Jacintha, our thoughts are with you and your family. From all your fellow nurses, we bless your soul. God bless."
Britain's Press Association reported she had a partner, Benedict Barboza, and a teenage son and daughter. In a statement, Saldanha's family said they were "deeply saddened" by the death and asked for privacy.
"She was a lovely, lovely person who always spoke to you when you saw her in the street," neighbor Mary Atwell told the agency. "She fitted in well around here, they all did. They've lived here for at least 10 years and were very quiet and pleasant."
During the call, a woman using the often-mimicked voice of Britain's monarch asked about the duchess' health. She was told by the second nurse who took the call from Saldanha that the duchess, the former Kate Middleton, "hasn't had any retching with me and she's been sleeping on and off."
The Australian Communications and Media Authority, which regulates radio broadcasting, says it has received complaints about the prank and is discussing the matter with the Sydney-based station, though it has not yet begun an investigation.
The station has a history of controversy, including a series of "Heartless Hotline" shows in which disadvantage people were offered a prize that could be taken away from them by listeners.
St. James's Palace, the office of the duchess and her husband Prince William, expressed sadness at Saldanha's death, but insisted it had not complained about the hoax. King Edward VII's Hospital said it did not reprimand Saldanha, nor had plans to discipline her.
Officials from St. James's Palace have said the duchess is not yet 12 weeks pregnant. The child would be the first for her and William.