Officers were called after “possible human remains” were found on Rowdown Fields in Croydon just after 9am on Tuesday.
Yesterday a 44-year old man and a 48-year-old woman were arrested on suspicion of murder and remain in police custody.
Scotland Yard said a post-mortem examination will begin today in a bid to identify the remains.
Detective Inspector Martin Thorpe said: “I understand the significant concern this discovery will have caused to local people.
“I want to thank the community for their patience. I can confirm our work at the location is complete.”
DI Thorpe added: “We believe that the remains found are those of one person.
“Although we are unable to formally identify the victim at this time, my team are working around the clock in order to do so.
“Their enquiries have made significant progress and I will provide a further update as soon as possible.
“We remain in contact with partners and local community members. I am grateful to them for their support.”
Anyone with information that may assist the investigation who has yet to speak with police is asked to call 101, quoting reference 1656/02Apr.