Scotland Yard appealed for information and asked for at least three witnesses believed to have been in the area to come forward.
Miss Nickell, of Tooting, south-west London, worked until recently as a model. She was attacked as she took a morning walk with her two-year-old son Alexander and their dog at about 10am on Wednesday.
'We urgently wish to interview a man who was apparently washing his hands in a stream close to Queen's Mere pond not far from the murder scene,' a Scotland Yard spokeswoman said.
'He is described as white, in his twenties, with short, tidy, brownish hair and wearing a light- coloured sweater and jeans. He was seen at about 10.40am and we want to eliminate him from the investigation. We believe at least three people may have walked past him and we urgently want them to come forward as well.'
Anyone in the area between 9.30am and 10.40am should contact the incident room at Wimbledon police station on 081-947 1212, the spokeswoman added.
A knife discovered in undergrowth on the common was being examined by forensic experts to determine if it was used in the attack. It was found 150 yards from the murder scene.
An elderly man stumbled on the body. Miss Nickell had been sexually assaulted and stabbed many times after putting up a fierce struggle, according to the police. Her son was clinging to her body. He is being looked after by his father, Andre Hanscombe, 29, a motorcycle courier, at the home of a relative.
Rachel's parents, Andrew and Monica Nickell, of Ampthill, Bedfordshire, were continuing a holiday in North America unaware of their daughter's death. They are driving with relatives in the remote Fingers Lake region, in upper New York state. Radio and television appeals have asked the couple to phone home.
State police in Albany said: 'It would be horrible if they found out about their daughter from anyone except the family.'
The murder has sparked widespread public revulsion and alarm among women. It was not just the youth and beauty of the victim; it was the apparent randomness of the attack, the brutality and the fact that it took place in daylight in a public place noted for its tranquility. And, perhaps above all, the fact that it was witnessed by the small boy.
The common is known to be frequented by flashers. The last murder took place there more than 20 years ago.
Elaine Radford, drinking a cup of tea outside the Windmill cafe, summed up the fears felt by women after the attack. 'We all know not to go down dark alleys but you just don't think anything could happen to you in a place like this in broad daylight.'
Flowers have been laid at the foot of an oak tree near the murder scene.
One note reads: 'May you rest in peace, you who were so cruelly taken from this beautiful place, and may God help us to find forgiveness for the wretched soul who took you from us.'