Police investigating the death of Sabina Nessa are at a flat in Eastbourne today.
The flat is in Terminus Road.
It has been searched and police are guarding the property.
The suspect was detained around 3am on Sunday morning in Eastbourne and is being held in 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.”