A 26-year-old man has been arrested on suspicion of murder following the death of Ann Widdecombe, police say.
Devon and Cornwall Police say a white British male is in custody after the 78-year-old was found at her home on Thursday with serious injuries.
The incident is not being treated as terrorism and there is "no information" to suggest it was politically motivated, they add.
Police say it is too early to comment on whether the suspect was known to Widdecombe.
PM Keir Starmer says the murder investigation is "shocking news", while Conservative leader Kemi Badenoch says she is "stunned" over the "horrific" incident.
Widdecombe, a former Conservative minister turned Reform UK spokeswoman, served as the MP for Maidstone in Kent for 23 years.
Farage pays tribute to 'remarkable' Widdecombe as he is 'deeply upset' by nature of death
Reform UK leader Nigel Farage has released a video statement describing Widdecombe - a spokesperson for his party - as having been an "extraordinary" and "remarkable, principled woman".
He says he is "deeply, deeply upset by the nature of her death," adding that she would "not have harmed a fly".
"She was kind to everybody. Frankly this was somebody who gave her life to public service, to fighting for the things that she believed in," he says.
Widdecombe also reached "way beyond politics", he says, describing her TV appearances in shows like Strictly Come Dancing and Celebrity Big Brother.
"She wasn't just a politician, she was a celebrity," he says.
"Our nation is a much, much poorer place without her. Reform UK is certainly a much worse place without her," he says, adding that he was expecting to see her in the next few days.
Green Party leader 'shocked at news about circumstances' of Widdecombe's death
Leader of the Green Party Zack Polanski says he is "shocked to hear the news about the circumstances of Ann Widdecombe's death".
"My thoughts are with her loved ones at this distressing time," he says in a post on X.
Widdecombe's home a short drive away from location suspect was arrested
A satellite image of the Haytor area in Dartmoor shows the location of Widdecombe's house, where she was found dead on Thursday.
The property is detached and in a remote location surrounded by neighbours and fields.
