Suzy Lamplugh, 25 was last seen with a man aged between 25 and 30, about 5'8" tall, with swept back hair and a dark suit outside a property in Fulham at 1300 BST two days ago.
A man called Mr Kipper had telephoned to book an appointment to view the house on Sherralds Road earlier on Monday.
Her colleagues at Sturgis estate agents became suspicious when Suzy did not return from her appointment - booked for 1245 BST - and missed a meeting with another client 1t 1800 BST.
Police revealed no Mr Kipper was known at the address he had given. They discovered Miss Lamplugh's car at 2200 BST that evening outside a property for sale in Stevenage Road, one-and-a-half miles away from her original appointment.
The car a B-registration, company owned, white Ford Fiesta - had been left with its doors open and Miss Lamplugh's purse in the door pocket. The ignition key was missing.
Detective Superintendent Nick Carter, in charge of the investigation said: "Everything leads us to believe she has been abducted."
Miss Lamplugh - had lived for a year in a two-bedroom flat she owned in Putney. At the time of her disappearance she was wearing a grey skirt, dark jacket and low stiletto heels.
Speaking at the family home in south west London her father Paul, a solicitor, said: "I don't think Suzy has been murdered. I believe she is still alive and with every body's help we will find her. Her mother Diana - founder of the British Slimnastics Association - fought back tears as she said: "There has never been a time in the past when I did not know where she was."
A former beautician on the QE2, her friends, family and colleagues describe her as a conscientious, outgoing and happy young woman.
It became the most well-publicised missing person case since that of Lord Lucan in November 1974. The police inquiry was called off a year after Suzy Lamplugh's disappearance, but police have said the file will remain open until a body is found or a suspect is conclusively identified.
Suzy Lamplugh was formally declared dead in 1994.
To watch an emotional appeal made by the parents of Suzy Lamplugh for her safe return, click on the video link below. (First broadcast 30 July 1986).