Detectives are investigating whether primary school teacher Sabina Nessa was killed by a stranger who is still at large, a senior officer has said.

The 28-year-old had been walking to meet a friend at a pub in Kidbrooke, south east London, on a journey that should have taken just five minutes when she was fatally attacked near Cator Park.

Speaking at the park where flowers had been laid beside a police cordon, Detective Chief Superintendent Trevor Lawry said he is “keeping a completely open mind” on what the motive of the attacker may have been but is concerned that they are still on the loose.

Asked whether the Metropolitan Police are worried that the killer could attack someone else, he said: “We have lines of inquiry that we’re pursuing at the moment.

“It’s always a concern that it may happen, but that’s not something that we have any intelligence on at this time.”

And asked whether he believes a stranger was behind the attack, Mr Lawry added: “That’s definitely a line of inquiry that we’re looking at.”

Ms Nessa’s body was found by a member of the public almost 24 hours after her death.

Asked by reporters why it took police so long to find her in a small and busy park, he said: “It was found by somebody walking their dog and it was off the track that you would normally walk so that’s not that unexpected.”

Her death comes just months after the killing of Sarah Everard, who was abducted in Clapham, south London, and just over a year after sisters Bibaa Henry and Nicole Smallman were murdered at a park in Wembley, north London.

Mr Lawry insisted the streets of the capital were safe for women and officers were listening to concerns.

He said: “The streets are safe for women, I’d like to reassure the public around that, I’d like to make sure that people are free to walk around free from fear and my officers will make sure that that can take place.”

On whether the Met had changed their approach to policing violent crime against women following these murders, he added: “I think the main things that are changing are that one, we’re listening to people, we’re understanding where people are feeling not so safe and we’re putting out patrols to make sure that we do that.

“This isn’t just a policing issue, there’s lots of issues to be able to make people feel safe in an open space and we’re working with our partners to ensure we do that.”

Downing Street said the Prime Minister’s thoughts were with the family and friends of Ms Nessa.

A spokesman for Boris Johnson said: “The Prime Minister’s focus is on making sure that we make our streets safe for absolutely everybody, that’s why we’re investing the money we are in recruiting more police officers and which is why we, as I say, introduced the strategy when it comes to violence against women and girls earlier this year.”

He added that Metropolitan Police officers will be attending a planned vigil for Ms Nessa on Friday.

Officers have said Ms Nessa left her home on Astell Road and was killed on her way to The Depot bar in Pegler Square, Kidbrooke Village, at around 8.30pm last Friday.

Her body was found near the OneSpace community centre at Kidbrooke Park Road in the Royal Borough of Greenwich at around 5.30pm on Saturday.

“Sabina never arrived at the pub and is thought to have been murdered as she walked through the park,” the force said.

A post-mortem examination, carried out on Monday, was inconclusive.

It came as Mayor of London Sadiq Khan said violence against women should be treated with the same level of priority as counter terrorism following the murder of Sabina Nessa.

Speaking to the PA news agency on Thursday morning, Mr Khan said: “I think we need to make sure we have a fully joined up policy to address this issue from school with boys being taught to respect girls and proper healthy relationship education, to the government outlawing misogyny and making it a hate crime and making the harassment of women in a public place a criminal offence, to making sure the police have the support they need to address violence against women and girls but also to making sure the criminal justice service gives this the seriousness it deserve.

“I think this deserves the same priority as counter terrorism. I agree with the inspector who called this an epidemic.

“I think it is an epidemic and I think it’s really important that people like me, who have not had to live the experiences of women and girls listen to the experience of women and girls and work with them to have policies that address this awful issue.”

He added: “I’m in close contact with the Metropolitan Police Service and my thoughts and prayers are with Sabina Nessa’s family. It’s just awful what happened to Sabina last Friday. When I think of Bibaa Henry, Nicole Smallman, Sarah Everard, it’s heart-breaking.”

Anyone with information is asked to call police on 0208 721 4266 or Crimestoppers anonymously on 0800 555111.