Police are investigating whether Sabina Nessa was killed by a stranger as she walked to meet a friend at a pub.
The body of the 28-year-old teacher was found by a member of the public in Cator Park, Kidbrooke, on 18 September.
Officers believe she was attacked shortly after leaving her Astell Road home at about 20:30 BST last Friday.
Speaking at a press conference, Detective Chief Superintendent Trevor Lawry said: “The streets are safe for women.”
He added: “People should be free to walk around free from fear and officers are here to make sure that can take place.”
Asked whether police believe Ms Nessa was attacked by a stranger, he said: “That is definitely a line of inquiry that we are looking at.”
A man in his 40s was who arrested on suspicion of murder the day after Ms Nessa’s body was found was later released under further investigation.
Meanwhile, the Royal Borough of Greenwich has said that over the next few days and weeks, the police and council enforcement officers will be conducting extra high-visibility patrols across Royal Greenwich and Lewisham.
Denise Scott-McDonald, Deputy Leader of the Council said: “We are appalled by the senseless murder of Sabina, a much-loved teacher who was killed while simply walking home through a park. This brutal and terrible attack reminds us why tackling violence against all women needs to be at the top of everyone’s agenda.”
Our number one priority is to make sure that people who live in and visit the borough are kept safe. This year, we began developing a new women’s public safety plan to improve how we understand and tackle the causes and consequences of violence against women. Some existing council funding has been used to support this work and we are waiting to hear the result of further external grants.
Jackie Smith, Cabinet Member for Community Safety and Enforcement said: “We want to reassure residents that we are doing everything we can to keep you safe following this horrific crime. Alongside many other projects including our integrated enforcement work with the police and a programme tackling the perpetrators of domestic abuse, we have also made a big investment to upgrade our existing CCTV system over the next few years. Old cameras have been replaced by new digital ones which now offer much clearer pictures, especially at night. This investment will help our staff and the emergency services to identify, respond, and resolve crime more effectively, and ultimately keep you safer.”
The police are appealing to the public for any information – no matter how seemingly small – to make sure we catch the person who committed this terrible crime.
Did you see someone loitering or acting suspiciously? Did you see anyone leaving the area in a hurry, perhaps running away? If you have any information, it is vital you tell the police: please call 0208 721 4266, or 101. Alternatively, you can contact Crimestoppers.