A man has been arrested on suspicion of the murder of Sabina Nessa, police have said.
The 38-year-old was arrested in East Sussex in the early hours of Sunday.
Ms Nessa’s family have been informed of this “significant development”, the Metropolitan Police said.
It is the third arrest police have made in connection with the 28-year-old’s murder.
The two other men arrested in recent days were both released pending further investigation,
A 38-year-old man was arrested on suspicion of murder at an address in East Sussex at around 3am on Sunday.
Ms Nessa, who taught at a primary school in southeast London, was attacked in the evening of 17 September after leaving her home in Kidbrooke to meet a friend at a nearby bar.
Police said her walk to The Depot in Peglar Square, Kidbrooke Village, should have taken just over five minutes.
Ms Nessa’s body was discovered in nearby Cator Park - where she is believed to have been attacked - the next afternoon.
On Thursday evening, investigators released CCTV images of a man they urgently wished to speak to, and one of a silver car they believed he had access to.
The Met said on Saturday evening that the balding man is believed to have been carrying a reflective red object that he may have been trying to conceal up his sleeve.
He was captured on CCTV as he walked through Pegler Square in Kidbrooke, south-east London, where Ms Nessa had been heading on the evening she died.
Scotland Yard would not confirm if the suspect was the man in the footage, but it is understood investigators are no longer seeking him taken into police custory, the Met said.
Additional reporting by Press Association