Officers are expected to terminate all existing lines of inquiry at the end of September, although the file will remain open for any new evidence.
A fresh investigation was ordered after 33-year-old Colin Stagg was acquitted of the murder of Ms Nickell at the Old Bailey in Septmber l994.
The judge condemned the use of an undercover policewoman who had tried to extract a "honey-trap" confession after befriending him.
Despite studying 7,000 inquiry files, 2,500 statements, and reports on more than 500 suspects, the new team has failed to find enough evidence to charge anyone.
Ms Nickell, 23, was killed in front of her then two-year-old son, Alex, who now lives with her partner Andre Hanscombe in France.
Both Mr Hanscombe and Ms Nickell's parents have been told of the police decision to shut down the inquiry.
A spate of civil actions may now follow. Ms Nickell's family are said to be considering suing Mr Stagg through the civil courts, while he in turn was granted legal aid after his acquittal to sue police for malicious prosecution, and wrongful arrest.Reuse content