The 78-year-old’s death was announced on Friday morning after the former MP was found at her home having sustained serious injuries.
A 26-year-old white British man was arrested at an address around 25 minutes away in Newton Abbot on Friday on suspicion of the murder.
Devon and Cornwall Police were called to her home in the rural village of Haytor in Dartmoor, Devon, and were joined by the the ambulance service at around 11.40am on Thursday where she was found dead.
They say her next-of-kin have been informed and are being supported by specially trained officers.
Assistant Chief Constable Longman said: "The suspect, who is a white British national, remains in police custody while inquiries continue."
He told reporters at a press conference: "Detectives from the force major crime investigation team have launched a murder investigation, and are conducting extensive inquiries into the circumstances surrounding Ms Widdecombe’s death.
"While we work closely with our partners and consulted counter-terrorism policing as part of our initial inquiries, the incident is not being treated as terrorism.
"A cordon remains in place at the property, while specialist officers continue forensic examinations.
"There are road closures in place around the scene, and the public will see significant police activity in the area while detectives and other officers continue house-to-house and CCTV inquiries.
"This is an extremely tragic incident. Our thoughts are very much with the family and friends of Miss Widdicombe in this very difficult time.”
A cordon remains in place at the property while specialist officers continue forensic examinations and road closures are in place around the scene.
Detective Chief Inspector Ilona Rosson said earlier: "This is an extremely tragic incident and our thoughts are very much with the family and friends of Ann Widdecombe at this difficult time.
"Our murder enquiry is in its early stages but moving at a significant pace. We are deploying all of the necessary resources to find out exactly what has happened and to locate the person responsible who we believe to be a white male.
"I would appeal to anyone who may have information about this incident, however insignificant it may seem, to come forward and speak with us.
"We are particularly keen to hear from anyone who may have seen anything suspicious in the vicinity of Haytor Vale, Haytor, or anyone with CCTV, doorbell or dashcam footage which could assist with our investigation.
"We have an increased uniformed police presence in the area to both support the investigation and provide reassurance to residents.
"Anyone with concerns can speak with our officers at the scene.“We will release further information when we are able to do so. In the meantime I would ask people not to speculate about what might have happened, particularly on social media."
Widdecombe’s management team, Cloud9 Management, said they were "absolutely devastated" by the news.
The statement said: "We are absolutely devastated by this news following a very traumatic and upsetting 24 hours.
"We fully support the police in their investigations and we reiterate the family’s desire not to be contacted at this difficult time. We implore anyone who may have relevant information to contact Devon & Cornwall Police."
Responding to the update, Sir Keir Starmer said he had spoken to Nigel Farage, Andy Burnham and Kemi Badenoch, describing it as a moment to "rise above any political differences".
He urged anyone with information to help police get the suspect into custody.
Announcing her death on Friday morning, her management said: "It is with great sadness that today we announce the death of the Rt Hon Ann Widdecombe, DSG.
"We send our deepest condolences to Ann’s family and friends. We ask that the family’s wish not to be contacted at this sad time is respected."
Throughout her political career, Ms Widdecombe was a prominent Eurosceptic and supported the Vote Leave campaign during the 2016 Brexit referendum.
She will also be widely remembered for her appearance on Strictly Come Dancing in 2010 where she was paired with professional dancer Anton Du Beke.
Despite low marks from the judges, she won support from viewers and lasted 10 weeks on the show.
Widdecombe also appeared on other TV programmes such as Celebrity Big Brother, hosted Have I Got News For You and the 2002 documentary When Louis Met... Ann Widdecombe with Louis Theroux.
She also appeared in a number of pantomimes alongside stars such as Basil Brush and Craig Revel-Horwood.
LBC’s Iain Dale wrote on X: "So sorry to hear about Ann, said the first text I saw this morning.
"Ann, who, I thought to myself, before I found out the awful truth. I say in my book that Ann Widdecombe is one of the handful of true friends I have made in politics.
"I am bereft at her loss. I’m about to write a full and lengthy tribute to a woman who remained true to herself, her values and her religion.
"I’m going to hugely miss her."
Her dance partner Du Beke paid his own tribute, writing on X: "Hi my loves, the saddest of news today of the passing of the lovely Ann Widdecombe.
"On behalf of myself and the whole family, our thoughts go out to her nearest and dearest and her whole family. We will all remember her fondly and miss her. Anton x."
Kemi Badenoch said: "I’ve been stunned to hear this awful news.
"To be honest, I’ve really struggled to find the words to say. Ann Widdecombe was a very fun and feisty woman who spoke her mind and she was 78 years old, she was an elderly woman."
She added: "The Conservative Party is reeling. Ann was a long-standing member of the Conservative Party, she was a Conservative minister, and then she moved to Reform.
"I’m sure they’re just as stunned as we are, and I extend my condolences to Nigel Farage and everyone in Reform on behalf of the Conservative Party, because we’ve both lost a friend."
A spokesperson for incoming PM Andy Burnham said: "Andy’s deepest condolences and thoughts are with Ann’s family today, in incredibly distressing circumstances.
"Ann gave a lifetime of public service, and it’s absolutely right that the police put all their resources into investigating this as swiftly as possible."

Politics Editor