A neighbour of Sabina Nessa says the route through Cator Park along which the 28-year-old teacher is thought to have been fatally attacked is "too dark."
Ms Nessa was walking from her home on Astell Road to meet a friend at The Depot, a bar near in Kidbrooke station, on a journey that should have taken just five minutes.
It is believed she crossed Cambert Way at around 8.30pm on Friday, re-joining a path leading to the back of OneSpace community centre, near to which her body was discovered at 5.30pm the next day.
Loye Olatunbosun, 26, who lives on Astell Road, said: “I walk in that direction very late at night often to get to Sainsbury’s.
“I walk through the first half of park, but never all the way through. It’s too dark there.
“I’ll usually cross over the grass to the main road and walk up there instead.
“This place is extremely safe so it’s quite shocking.
“It’s a family neighbourhood. I’ve never heard of anything like this.
“Before it was renovated, maybe, but since it was redeveloped its largely families with kids living here.
“It’s unfortunate that as a woman you always have to be cautious.
“I’m not sure if I’ll be walking through the park at all in the future.”
An extensive police cordon is in place surrounding the OneSpace community centre, near to which flowers have been laid alongside tributes.
Detectives are investigating whether the primary school teacher was killed by a stranger who is still at large.
Speaking at the scene, Detective Chief Superintendent Trevor Lawry said police are “keeping a completely open mind” on what the motive of the attacker may have been.
Asked whether the Metropolitan Police are worried that the killer could attack someone else, Mr Lawry 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 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, Mr Lawry 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.”
A vigil is due to take place on Friday evening at Pegler Square, outside The Depot, in Sabina's memory.
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