The former Conservative minister and later Reform UK spokeswoman was found dead at her home in rural southwest England about 11.40am on Thursday with what police described as "serious injuries".
Assistant Chief Constable Matt Longman said a 28-year-old white British man was arrested on suspicion of murder in Rotherham, South Yorkshire, shortly after 9pm on Saturday with the support of Counter Terrorism Police.
He told reporters on Sunday: "At this point, there is still no information to suggest that this is a terrorism-related incident and at this point we are not looking for anyone else in connection with this murder.
"At this stage, there is nothing to suggest that it was politically motivated."
He said Devon and Cornwall Police detectives "remain open-minded about the potential motive" and stressed it is not believed there is any threat to the wider public.
"We are aware of online and public speculation, particularly with regards to motive," he said.
"Again, I urge people not to share or engage with that speculation - it's unhelpful, it doesn't aid our investigation, and particularly, it's distressing to the family and friends of Ms Widdecombe."
Police said previously it is believed Widdecombe was attacked on Wednesday at 12.30pm.
Widdecombe, who was 78, was first elected a Conservative MP in Kent in 1987, went on to serve as a member of the European parliament for the Brexit Party and then a spokeswoman for Reform UK.
She also found fame outside politics after starring in Strictly Come Dancing and Celebrity Big Brother.
Speaking on Sunday, Chief Constable James Vaughan, of Devon and Cornwall Police, said the force has "mounted an extraordinary response to a horrific murder of a very prominent public figure".
"The operation has been running at a lightning pace for 48 hours," he said.
"I am really pleased that we have a suspect firmly in custody and that will undergo some further work from us today.
"Well done to all - this is clearly British policing at its very best."
Widdecombe's personal driver of 10 years, Peter Horrell, lay flowers in front of her home on Saturday.
Speaking to reporters, Horrell said the politician "never mentioned any fear" for her safety and loved living in the village of Haytor.
Reform UK party leader Nigel Farage also visited the village to pay tribute to Widdecombe on Saturday.
He told reporters that the party has been going through its emails to check for patterns of abuse directed at Widdecombe but has not been able to find anything.
Reform's MPs are now being given 24-hour security protection following her death, it has been reported.
ITV News has published a series of WhatsApp images which appear to show that Widdecombe stopped responding to messages from a TV producer after the approximate time police believe the attack took place on Wednesday.
CCTV footage seen by The Telegraph appears to show a man leaving an address linked to the suspect at about 7am on Wednesday, the newspaper reported.
The man was seen putting "some kind of wooden stick" into the passenger side of a red car before driving off, neighbours said.
with Reuters
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