Ms Waddell had studied social and political thought
A 29-year-old woman whose body was found following a fire at her flat in Brighton was strangled, police said.
The body of Andrea Waddell, who had a masters degree but worked as a prostitute, was found just before midnight on Thursday by firefighters.
Police started a murder inquiry after a post-mortem examination on Friday.
Det Ch Insp Adam Hibbert appealed for other members of the city's sex industry to come forward if they had information about Ms Waddell's death.
He said Ms Waddell moved to Brighton about five years ago to study at the University of Sussex after gaining a degree in philosophy at Durham University.
She was sociable and well-known, but was not known to drink or take drugs he said.
"However, there was another side to Andrea's life, and we believe that Andrea was a sex worker.
"Our priority is to find the person who murdered Andrea.
"We need the public's help - particularly within the sex worker community, there may be people who have vital information about Andrea's death.
"Andrea did not deserve to be murdered. We will find her killer."
Forensics officers were expected to be at the first floor flat in Upper Lewes Road for many days, he said.
It is not known how the fire started or whether it was started deliberately. It was contained in Ms Waddell's bedroom.
She was last seen alive some time on Thursday. Her car has been towed away for examination.
Close to family
Mr Hibbert said she was "discreet" about her work, but was known sometimes to take clients home with her.
He did not disclose what was used to strangle Ms Waddell or whether her body was set on fire.
Ms Waddell, who grew up in Reading, Berkshire, with her parents, Sonia and Robin, and brother, Nick, was described as being very close to her family.
A statement from her family said: "We want the world to know how much we love her and how proud of her we are and always will be.
"She endured so much pain and suffering in her life - she still had constant pain - and was brave, resilient and loving."