Anne Widdecombe was killed in a "targeted attack" and detectives are still working to understand the motive, police have said.

Assistant Commissioner Laurence Taylor, Head of Counter Terrorism Policing, said the appearance of the former Conservative minister turned Reform UK spokeswoman on Talk TV on the morning she was killed at her home in Devon is being looked into as part of the investigation.

In an update at New Scotland Yard, he said he could not comment when asked if the killer could have been targeting other Reform figures.

Detectives have obtained a warrant under the Terrorism Act to hold the 28-year-old suspect arrested in Rotherham on suspicion of murder for up to seven days.

The body of Widdecombe, 78, was discovered on Thursday 9 July at her home in Haytor. She had sustained serious injuries in an attack police believe took place the previous day.

A white British man, 28, was arrested on Saturday. He was re-arrested on Monday on suspicion of the commission, preparation or instigation of acts of terrorism.

Taylor said a counter-terrorism investigation is "running in parallel" to the murder investigation but the suspected killing "has not been declared a terrorist incident at this stage".

He told reporters: "It is clear that this was a targeted attack. We are still working to understand the extent of any planning or preparation, and the motivation that sits behind that attack.

"I wouldn't want to comment on what that motivation was."

Taylor added: "There are multiple lines of inquiry that we are pursuing expeditiously, and that includes a number of digital forensic examinations."

The counter terrorism police chief said he did not want to rule out anything, and would not comment on whether they were investigating whether a foreign state was involved.

"We are working through what the motivation for the attack currently is", he said.

Taylor also refused to comment further on details about the planning and preparation of the attack.

On Monday, Home Secretary Shabana Mahmood told the House of Commons the suspect was not known to the government's Prevent anti-terror scheme.

Taylor would not comment on whether the arrest on suspicion of terror offences means the suspect potentially committed terrorism offences separate to the murder case, or whether any other politicians were potential targets.

He said: "This is a murder investigation following a brutal attack on a 78-year-old woman in her own home."

There has been a "deeply distressing impact on Miss Widdecombe's family", he added.

On Widdecombe's Talk TV appearance, Taylor said: "We are exploring all lines of inquiry and that is one of the lines of inquiry that we'll be exploring."

He said: "My request is that we don't over speculate and that we go where the investigation takes us. In terms of motive it would be wrong for me to ascribe either an ideology, or what the motivation might be at this stage."

Counter-terror police took over the investigation into Widdecombe's death from Devon and Cornwall police on Monday.

The development followed an earlier statement from Devon and Cornwall Police that, while they were keeping an open mind, there was "nothing to suggest" the murder was politically motivated.

Taylor told reporters: "Based on new information we felt it was appropriate that we took over the investigation."

In an earlier statement, Devon and Cornwall's police and crime commissioner defended the force after the investigation was handed over to counter-terror officers.

Alison Hernandez acknowledged "commentary" about the way police communicated during the early stages of the case, but described the force's response as "substantial and professional" and said it was "not unusual" for counter-terror police to become involved later.

It has also emerged that Widdecombe, who served as Conservative MP for Maidstone in Kent for 23 years, gave a pre-recorded radio interview about 20 minutes before police believe she was attacked.

She spoke to British Christian radio station TWR-UK for about nine minutes via video link, but the interview was not broadcast.

The station later shared part of the recording with Times Radio, which first aired the interview on Tuesday.

In the interview, she spoke about her support for Reform UK leader Nigel Farage following his decision to re-fight his Essex seat in a by-election, amid scrutiny over his finances and a parliamentary investigation.