The woman has now been identified as 28-year-old Sabina Nessa from Kidbrooke.
A post-mortem examination carried out at Greenwich Mortuary on Monday, 20 September was inconclusive.
Next of kin have been informed and are being supported by specialist officers.
The investigation is led by Detective Chief Inspector Joe Garrity from the Specialist Crime Command. He said: “Our initial enquiries suggest that this attack happened at around 20:30hrs on Friday, 17 September, a time when the park was likely being used by many people from dog walkers to joggers.
“Sabina was found near the OneSpace community centre which we know is a facility used by lots of people and we would ask anyone who was in or around the area and who may have any information to come forward.
“Did you see someone loitering or acting suspiciously? Or, did you see someone leaving the area in a hurry, perhaps running away? If you have any information, it is vital you tell us.
“We are working around the clock to deliver justice for the family of this young woman, and we need your help to do it. Please contact 0208 721 4266, or 101. Alternatively contact Crimestoppers.”
Chief Superintendent Trevor Lawry, responsible for local policing in Greenwich, said: “Our thoughts are first and foremost with Sabina’s family and friends following this shocking incident and we will continue to provide our support to them as the investigation progresses.
“We know this incident will be worrying to those who live and work in the community. Over the next few days, they can expect to see extra high-visibility patrols both in and around the crime scene as well as other open spaces across the boroughs of Lewisham and Greenwich.
“As always, we are also working very closely with both local authorities to speak to our communities to ensure we are doing everything possible to keep people safe.”
A man, aged in his 40s, arrested on suspicion of murder has been released under investigation pending further enquiries.
A number of crime scenes are in place and enquiries are ongoing.