Officers investigating Kellie Telesford's death are now treating it as murder.
Kellie Telesford, a transsexual who had been living as a woman for a number of years, was found strangled at her home in Leander Road, Thornton Heath, on Wednesday.
Police had visited the 40-year-old's home after being contacted by concerned friends.
Detectives are now keen to speak to anyone who had contact with Kellie, born Kayiode Dexter-Telesford, between November 15 and 21.
Detective Chief Inspector Cliff Lyons, from the Homicide and Serious Crime Command who is leading the investigation, said: "We would also like to speak to anyone who knew or who has had a relationship with Kellie to help us build a picture of her lifestyle.
"We know she went to venues popular with the lesbian, gay, bisexual and transgender communities, in particular in the Croydon and Brixton area.
"There are several lines of enquiry that we are following, but help from the community is still paramount. I would also like to reassure all parts of the community affected by Kellie's murder that our dedicated team of detectives are committed to finding the person responsible.
"The lesbian, gay, bisexual and transgender liaison officers on borough are aware and are acting as a line of communication to and from the investigation team, ensuring any fears can be addressed. It should be stressed though that we have not seen any further incidents similar to Kellie's murder."
Anyone with information should call 020 8721 4205, or Crimestoppers on 0800 555 111.
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