Valerie Graves, 55, had significant head and facial injuries when she was discovered at the waterside house in Bosham, near Chichester, West Sussex, on Monday morning.
Detective Superintendent Nick May of Sussex Police appealed for information about anyone who saw someone with “blood-stained clothes” or who has been asked to wash or dispose of clothing “in unusual circumstances” to contact them.
He said he could not rule out that the killer was unconnected to Ms Graves or her family, but said officers were also investigating whether the murder was connected to something in her past or to someone she knew recently.
Police have a “large number of inquiries ongoing and a large number of forensic inquiries ongoing”, including the potential of a break-in, Mr May said.
The mother of two had been house-sitting with three other members of her family over Christmas while the owners of the detached family home were abroad.
Mr May said: “One of the lines of inquiry is that this act has been committed by somebody unconnected to Valerie, and yes that is a possibility.
“I’m not going to go into the specifics of how somebody may or may not have entered the house.
“We’ve got a large number of inquiries ongoing.”
Appeals from family, police
Speaking at the police press conference, Ms Graves’ son, Tom Wood, said his mother had recently moved back to Sussex from Scotland to be closer to her family.
“My mum was much loved and will be sorely missed by the whole family,” he said.
“She was a free spirit who enjoyed her life and was a talented artist.
“She had lived in Scotland for about 10 years, a place she loved and which inspired her passion for art.”
He added: “This has been devastating for the family and has come as a complete shock.
“We would appeal to anyone who has any information about this, no matter how trivial it is, to contact the police to help us catch whoever has done this horrible act.”
Ms Graves went to bed at 10pm on Sunday December 29 and was found dead by one of the three members of her family she was staying with at around 10am the following morning.
Mr May revealed that she was discovered in the bedroom in which she was sleeping at the rear of the house but declined to disclose whether she was in bed.
The relatives who were also staying at the property were her mother, sister and her sister’s partner, police have disclosed.
No arrests have been made, but Mr May said “significant” resources have been deployed involving detectives from across Sussex and Surrey.
Asked about any recent threats against Ms Graves, Mr May said: “We are doing an awful lot of work trying to understand about Valerie’s life, who she associates with and who may be connected in that way.”
He added: “We have got a significant number of officers searching the area at the moment. We have got a specialist underwater search team working. Bosham is almost under water at the moment, and we have got a large number of officers out there looking for items which may be connected with the murder.”