Counter-terrorism police are probing whether the suspect held over Ann Widdecombe’s killing was motivated by left-wing extremism and planning further violence against other high-profile figures.

Detectives confirmed Miss Widdecombe’s death was a “targeted attack”, and said whether the suspect in the alleged murder was targeting Reform UK figures will be a “line of investigation”

The police investigation is also probing whether left-wing extremism or other political motives were behind the killing, it has been reported.

The 78-year-old former MP and MEP was found dead at her home in Haytor on Dartmoor, Devon, on Thursday.

A 28-year-old white British man arrested in South Yorkshire on Saturday remains in custody.

He is being held on suspicion of commission, preparation, or instigation of acts of terrorism, as well as on suspicion of murder.

Counter-terrorism police are now in charge of the case after new evidence came to light – but a senior officer stressed the murder and terror investigations are currently working “in parallel”.

Assistant Commissioner Laurence Taylor told reporters on Tuesday the question of whether a TV appearance might have motivated her killing is also a “line of inquiry”.

Miss Widdecombe spoke to Mark Dolan by video-link on Talk TV just after 8am on Wednesday, and police believe she was attacked at about 12.30pm the same day.

“It is clear that this was a targeted attack,” Mr Taylor said.

“We are still working to understand the extent of any planning or preparation, and the motivation that sits behind that attack.”

Asked if police were probing whether the suspect was targeting other Reform UK figures, he said: “So clearly, part of our responsibility when investigating offences of this nature is to assure ourselves and therefore the public and others of any extant of threat.

“That will form a line of investigation to ensure that we are putting all appropriate measures in place to mitigate any threat, should it become apparent.

“I’m not saying there is or there isn’t at this stage.”

Incoming prime minister Andy Burnham said after the update that a “serious review” was needed into MPs’ security.

He said: “It’s obviously appalling what happened to Ann. I knew Ann over many years in the House, and you know, we would get along – and everybody would get along.

“But it feels as though something has changed. It’s easy to blame social media, but it feels like it’s having some impact in just building that kind of toxicity that’s around the political debate.”