A search for the Nickells, who have been travelling in remote areas of North America, ended on Sunday when they returned to friends in the Ontario area. Only then did they find out that their 23-year-old daughter had been murdered last Wednesday.
They were understood to be taking comfort from their son Mark, who flew to Toronto on Sunday with two Scotland Yard detectives.
Although the Nickells were initially told of Rachel's death by local police, it was left to their son and the Scotland Yard officers to break the full details to them.
Rachel's two-year-old son, Alexander, was found clinging to the body of his mother on the common in south-west London. Her throat had been slashed in a frenzied sexually motivated attack.
Detectives in London are deciding whether to stage a reconstruction of the crime tomorrow - a week after the murder - in an attempt to jog the memories of potential witnesses. They have issued a description of a man seen washing his hands in a stream on the morning Miss Nickell's body was found on the common.
Scotland Yard said at least three people were thought to have seen the man near the murder scene. He is described as white, in his twenties, with short, tidy, brownish hair. He was wearing a light-coloured sweater and jeans.
Police think Miss Nickell, of Tooting, south-west London, was attacked shortly after 10am as she walked with Alexander and their pet dog. A knife discovered in undergrowth on the common has been examined by forensic science experts in an attempt to determine if it was used in the attack.