The body was found Sunday by a member of the public walking a dog near the village of Anmer, which lies within the bounds of the 20,000-acre Sandringham estate in the English county of Norfolk.
A post mortem examination revealed the remains are those of a white woman aged 15 to 23, between 5 feet 4 inches and 5 feet 6 inches tall, with high cheekbones, Norfolk Police said.
But tests have so far failed to yield a DNA profile that might lead to her identity.
Further tests on bone material are being carried out as part of the murder investigation.
Police say it is “highly unlikely” the woman’s death was through natural causes, but there is no evidence of injury through firearms, a knife or other trauma such as broken bones.
The remains are thought to have been at the site for between one and four months. A specialist from the Natural History Museum will carry out more tests Friday to try to refine the estimate by studying insect life.
Speaking to reporters, Detective Chief Inspector Jes Fry said police were looking at people who might have been working or held events in the area, near the town of King’s Lynn, in August or September last year.
“We would be interested to hear from anyone who held or was involved in organizing any kind of function at Sandringham or neighboring parishes,” he added.
But Fry urged the media not to speculate about the woman’s identity to avoid causing distress to the families of missing people.
Sandringham House, at the heart of the rural estate, is where the royal family traditionally gathers to celebrate Christmas. It’s been the private home of four generations of British monarchs since 1862, and is one of two private residences used by the queen. Part of the estate is a 600-acre country park open to the public.
A Buckingham Palace spokesman told CNN Tuesday Queen Elizabeth and Prince Philip “are in residence at Sandringham from mid-December to the end of January” but could not confirm whether or not they had been informed of the murder investigation.
Prince Philip has been recuperating at Sandringham since he was released from the hospital December 27 after having a coronary stent implanted.
Sandringham House and its gardens are open to the public from April to November.