The last movements of Miss Nickell, 23, who was raped and stabbed to death in front of her two-year-old son Alex, were re-enacted by a woman who met her while walking her dog on the common in south-west London.
The woman, who wished to be known only as Jane, parked Miss Nickell's silver Volvo in a car park near the common and walked to the spot in a small wooded area where she was murdered.
The three-year-old son of a Wimbledon police officer played the part of Alex. The two were accompanied by a black dog similar to the one Miss Nickell regularly walked on the common and which was with her when she died.
Detective Superintendent John Bassett, who is heading the investigation, said the murderer clearly needed medical help. 'If he has got the last shreds of human decency, he will give himself up.'
Det Sup Bassett said that police were still interviewing people who had been on the common at the same time as Miss Nickell. He said there were some 'key suspects' and police still urgently wanted to talk to a man seen washing his hands in a stream and three people seen walking past.
He warned women to keep away from secluded areas of the common: 'I don't want to heighten the fear, but they should take care when out walking.'
Alex, who was found clinging to his mother's body, was said by Det Sup Bassett to be 'standing up well'.