A 38-year-old man has been arrested on suspicion of the murder of the London schoolteacher Sabina Nessa, Scotland Yard has said.

The man was arrested at 3am on Sunday at an address in East Sussex in what police described as as “significant development”.

DCI Neil John, from the Metropolitan police’s specialist crime command, said: “Sabina’s family have been informed of this significant development and they continue to be supported by specialist officers.”

The man has been taken into police custody where he will be questioned. He is the third man arrested over the killing.

Nessa, 28, is suspected to have been killed as she made what should have been a five-minute journey on foot to a pub from her home, at about 8.30pm last Friday.

She was found dead the following day in Cater park, in Kidbrooke, south-east London, where about 500 mourners held a candlelit vigil in her memory on Friday.

The killing has reignited concerns about the level of danger women face in Britain.

Two men previously arrested by homicide detectives – a 38-year-old man and a man in his 40s – have been released under investigation.

The latest arrest came 48 hours after police appealed for help to trace a man captured on CCTV images taken near where Nessa was found dead.

A 12-second video released by the Met shows the balding man wearing a black hooded coat and grey jeans looking over his shoulder and pulling at his hood as he walks down a footpath.

Nessa’s sister, Jebina Yasmin Islam, issued a statement on Friday evening before a rally at the East London Mosque – one of many vigils that took place across the country.

“We as a family are shocked of the murder of our sister, daughter and aunty to my girls. There are no words to describe how we are feeling as a family at the moment,” she said.

“We did not expect that something like [this] would ever happen to us. I urge everyone to walk on busy streets when walking home from work, school or a friend’s homes. Please keep safe.”

She added: “I ask you to pray for our sister and make dua [supplication] for her. May Allah grant her paradise.”