Former MP and MEP Ann Widdecombe is believed to have been attacked in her home nearly 24 hours before her body was discovered.
The 78-year-old was found dead at her house in Haytor on Dartmoor at around 11.40am on Thursday, having sustained serious injuries.
Police now believe the attack took place on Wednesday, at around 12.30pm.
Assistant Chief Constable Matt Longman of Devon and Cornwall Police said: "Our inquiries are moving at pace for a suspect who is believed to be a white male."
He added: "We do not believe there is a wider risk to the public."
Ms Widdecombe, who began her political career as a Conservative MP in Kent in 1987, later served as an MEP for the Brexit Party and was a spokeswoman for Reform UK.
She also became a familiar face outside politics through appearances on Strictly Come Dancing and Celebrity Big Brother.
A 26-year-old white British man was arrested at an address in Newton Abbot on suspicion of the murder of Miss Widdecombe on Friday but was released from custody on Saturday.
Assistant Chief Constable Longman said: "Our priority remains identifying those responsible and ensuring that all available evidence is thoroughly examined.
"Detectives continue to carry out numerous inquiries as part of the ongoing investigation and we remain committed to establishing the full circumstances surrounding the incident."
He said the investigation was "moving at a significant pace" and urged the public not to speculate.
Mr Longman said: "I would appeal to anyone who may have information about this incident, however insignificant it may seem, to come forward and speak with us.
"In the meantime, I would ask people not to speculate about what might have happened, particularly on social media.
"This is not only potentially harmful to our investigation but also deeply distressing for family and friends of Miss Widdecombe."
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He confirmed that a major incident public portal has been set up on the force’s website for people to submit information, images, or footage.
Police have said the case is "not being treated as terrorism", and there is currently "no information" to suggest the killing was politically motivated.
Information can also be passed anonymously to Crimestoppers.
The family has requested privacy as they come to terms with Ms Widdecombe’s death.
