Kerry Scott, 24, was last seen alive around 1.30am walking home with 29-year-old Richard Tate after celebrating New Year at the pub in Waterlooville, Hampshire where she worked.
Her body was discovered around 9.20am on New Year's Day at a lodging house in the town - a suburb of Portsmouth - by a relative who became concerned after she failed to answer the telephone.
Kerry had been severely beaten and stabbed with a sharpened blade.
Detectives investigating the murder have spent the day trying to trace Mr Tate, who lived a few doors away from the victim.
Dramatic phonecall
A Hampshire police spokeswoman said a man claiming to be Mr Tate had contacted the incident room on Saturday.
Detective Superintendent Des Thomas, who is leading the investigation, said: "We are concerned for his welfare and his apparent state of mind.
"We are keen to make further contact with Mr Tate. The quicker he gets in touch the quicker we can sort this out."
Mr Tate, who had been celebrating New Year with Kerry at The Centurion pub in Waterlooville, is believed to be in London.
Det Supt Thomas said: "Kerry died as a result of a violent attack for which there is no clear motive at this time."
He appealed to anyone who was in the Centurion pub on New Year's Eve or in the Crookhorn area of Waterlooville on New Year's Day.
Fifty detectives are working on the case and have been carrying out house-to-house inquiries in the area.
Anyone with information about the murder should contact the incident room at Fratton police station in Portsmouth on 01705 891651.
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