Police have named victim Sarah Mayhew after human remains were found in a park in Croydon last week.
The family of the 38-year-old, from Croydon, have been informed of her death and are being supported by specially trained family liaison officers.
Police have arrested a 44-year-old man and a 48-year-old woman on suspicion of murder.
Both suspects remain in custody pending further enquiries.
Detective Inspector Martin Thorpe, who is leading the investigation, said: “My thoughts are with Sarah’s family as they deal with this heartbreaking news.
“No family should have to lose a loved one in such tragic circumstances, and we will continue to provide our support as our investigation progresses.
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“The two people in custody were known to Sarah and at present we are not looking for anyone else in connection with her death.”
Chief Superintendent Andy Brittain, lead for policing in Croydon added: “While I hope these updates will offer some reassurance to the local community, we are aware of the understandable concern this incident has caused across New Addington.
“Your local policing teams will continue to be visible and available to discuss your concerns, and answer any questions you may have as best we can.
“We repeat our thanks for the support and patience of the public, which has allowed officers to carry out important enquiries at the scene.”
Police were called to the South London park last Tuesday
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Local resident Becky Phillips described the discovery as “awful”.
Another, Deb Watts, also told the Daily Mail: “This is so sad, thoughts are with the family.”
Police are urging anyone with information that may assist the investigation to call 101, quoting reference 1656/02Apr.
