The 38-year-old's body was found by her father at a house on Shearman Street in Trowbridge last Thursday.
A 78 year old man - who is not related to Ms Barker - was arrested on suspicion of manslaughter and actual bodily harm, police said.
He has since been bailed until the end of November, pending further enquiries.
In a statement Ms Barker's family said it had been "left devastated" by her "untimely death".
"She was much loved and will be greatly missed by us all.
"She was a bright young woman who, in addition to her attainment of a BSc degree in Dental Technology at the University of Wales Institute Cardiff, was a talented artist and an accomplished cook, having appeared on the Masterchef television programme.
"It will be difficult to come to terms with her loss, but this is being aided by the kind words and messages of support we have received and for which we are very grateful."
The family of Masterchef contestant Helen Barker have paid tribute to "a talented artist" after she was found dead at her home in Wiltshire.