Det Chief Insp Charles King, of the Homicide and Serious Crime Command, said: "I would like to appeal to anyone who was in the Limpsfield Avenue area between 5am and 6am to make contact with us.
"Lots of people would have been out and about at that time of the morning, either on their way to work or walking dogs - they may have noticed a woman dressed so distinctively.
"Did you see a black woman around that time wearing a leopard-skin print dress and no shoes? If so, we want to hear from you."
Ms Duncan-Bailey left her children, boys aged two and seven, with a friend in Bromley while she attended a family function, police said. She left the friend's at about 4am on Wednesday to return to Thornton Heath, where at about 4.30am she visited her former partner's home.
Police were called after reports of a domestic incident and Ms Duncan-Bailey left the address with officers. It is believed she asked to be taken to another friend's house in Limpsfield Avenue, Thornton Heath, and she was last seen between 5am and 5.30am walking towards flats in Limpsfield Avenue.