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A 38-year-old man has been arrested on suspicion of the murder of Sabina Nessa, police have confirmed.
The Metropolitan Police said the man has been taken into custody after being arrested at around 3am on Sunday 26 September at an address in East Sussex.
Detective Chief Inspector Neil John, of the force's Specialist Crime Command, said: "Sabina's family have been informed of this significant development and they continue to be supported by specialist officers."
Nessa, 28, had been walking to meet her friend at a pub in Kidbrooke, south east London, on Friday 17 September.
Her body was found near the OneSpace community centre at Kidbrooke Park Road in the Royal Borough of Greenwich the following afternoon.
Two other men - one aged 38, another in his 40s - had previously been arrested on suspicion of Nessa's murder, but were later released, pending further investigation.
Police also issued CCTV images of an unknown man walking in Pegler Square, Kidbrooke, on the evening Nessa was killed, as well as an image of a silver vehicle they believe he has access to.
At the time, DCI John said: "Our team have been working tirelessly to find the person responsible for Sabina's murder and this has included an extensive trawl of CCTV, work which remains ongoing.
"We would ask anyone - especially those in Kidbrooke and the wider area of Lewisham and Greenwich - to take a careful look at these images to check whether you know who this man is or have seen him over recent days.
"Any information as to his identity or whereabouts could be vital for our investigation so we are asking you to share this image far and wide to ensure as many people as possible see it."
Nessa's cousin, Zubel Ahmed, previously said that her parents are 'inconsolable' after their loss.
In an interview with the BBC, he said: "We are all truly devastated. Her parents are absolutely shocked, they're inconsolable still and understandably so, to hear of their daughter being taken away from them by some cowardly man is just horrific.
"She's been teaching for two years. Loves teaching, loves kids, she's got a couple of cats at home. She was just a beautiful soul.
"She honestly was the most caring person, kindest, sweetest girl you could meet. Sabina's heart was as good as gold, she never had a bad word to say about anyone. Her sister is going to miss her so much."
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