Owami Davies, 24, was last seen in West Croydon on July 7 after leaving her family home in Grays, Essex.
Her relatives have not heard from her, and she has not reported to work, according to the Metropolitan Police.
Detectives are currently conducting an investigation on Derby Road in West Croydon.
Two men, aged 23 and 27, were arrested in Croydon on Monday.
Both are being held in a police station in south London, along with a third man, 32, who was arrested on Tuesday.
Detectives from the Specialist Crime Command are leading the search for Ms Davies because they have the resources and expertise needed for a complex investigation, according to the Met.
Essex Police first reported Ms Davies missing on July 11. According to the police, she left the family home in Chafford Hundred, Grays, on July 4.
Essex Police said in an updated statement on July 16 that Ms Davies was last seen in Croydon on July 6. She was dressed in a black jumper, grey joggers, and a grey cap.
The Met issued its first public appeal on July 31, stating that Ms Davies was last seen on Derby Road in West Croydon shortly after midnight on July 7.
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