Sabina Nessa is thought to have been murdered as she walked through a park on her way to meet a friend at a pub, police said.

Officers investigating the 28-year-old teacher’s death said she left her home before walking through Cator Park in south-east London at about 8.30pm last Friday. She was heading towards the Depot bar in Pegler Square, Kidbrooke Village, when she was attacked.

Her body was found near the OneSpace community centre at Kidbrooke Park Road in the Royal Borough of Greenwich on Saturday, the Metropolitan police said. “Sabina never arrived at the pub and is thought to have been murdered as she walked through the park,” they added. A postmortem examination, carried out on Monday, was inconclusive.

A man in his 40s who was arrested on suspicion of killing her has been released under further investigation.

DI Joe Garrity said: “Sabina’s journey should have taken just over five minutes but she never made it to her destination. We know the community is rightly shocked by this murder – as are we – and we are using every resource available to us to find the individual responsible.”

He said the investigation was making good progress and they “believe there are still others out there who may have information that could help”. “If you think you saw Sabina or any suspicious behaviour in or around the park on Friday evening please speak to us.”

The London mayor, Sadiq Khan, said violence against women was a national “epidemic”. Appearing on ITV’s Good Morning Britain, he said: “Between last year’s International Women’s Day and this year’s International Women’s Day, 180 women were killed at the hands of men across the country.

“We do have an epidemic when it comes to violence against women and girls. I think us men have got to be allies in addressing this issue.”

Colleagues and neighbours have paid tribute to Nessa. Her colleague Lisa Williams, the head of Rushey Green primary school in Lewisham, called her a brilliant teacher and said the school had been left “devastated”.

Annie Gibbs, the vice-chair of the Kidbrooke forum community group, said people in the area were feeling shocked and scared. “We are a loving community and we have a strong sense of solidarity,” she said. “Everyone wants the same thing – to support Sabina’s family and to make sure that we find whoever did this so that she can get justice.”

She added: “We want people to respect and honour her life and make sure that we send a loud and clear message that we are a united community and this violent act isn’t going to divide us. Violence isn’t welcome here and we will stand up against it. Although many people didn’t know Sabina, our community is one.”

A vigil will be held at 7pm on Friday evening in Pegler Square for Nessa, supported by the group Reclaim These Streets, which organised a similar vigil after the murder of Sarah Everard in March.

Campaign groups have said that for too long the burden of women’s safety has been on women, adding that a woman dies at the hands of a man every three days in England.

The government released a violence against women and girls strategy (VAWG) in July and promised better support services for minority communities, as well as a public health campaign that will focus on perpetrator behaviour.

Gibbs, the founder of the community interest company Amour Destine, which supports black women and girls, said despite growing anger about violence against women the government was still not listening.

“The focus is still very much about making women feel safe, and we’ve got great strategies around that. But how much longer is it going to be women’s responsibility to keep themselves safe? What we need is a strategy that is going to focus on stopping people’s harmful behaviours.”