A man has been arrested on suspicion of murdering Sabina Nessa in what police say is a "significant development" in the case.
The 38-year-old was arrested at around 3am on Sunday at an address in East Sussex. He has been taken into police custody.
Detective Chief Inspector Neil John, from the Met’s Specialist Crime Command, said: "Sabina’s family have been informed of this significant development and they continue to be supported by specialist officers."
Hundreds of mourners gathered for an emotional candlelit vigil in memory of the "amazing, caring, beautiful" primary school teacher Ms Nessa on Friday.
Family members wiped away tears as they spoke movingly of the sorrow the 28-year-old's murder had caused.
The Duchess of Cambridge shared a personal message on Twitter, describing how she was "saddened by the loss of another innocent young woman on our streets".
Ms Nessa had been walking to meet a friend at a pub near her home in Kidbrooke when she was fatally attacked.
Her body was discovered by a member of the public the next day in Cator Park, having been hidden under a pile of leaves, it was reported.
Two men were separately arrested on suspicion of her murder but were subsequently released under investigation.