Former Conservative minister Ann Widdecombe was killed in a “brutal” and “targeted attack”, the head of counter terror policing said on Tuesday, as officers continued a parallel investigation into whether terrorism-related offences were involved.

Assistant Commissioner Laurence Taylor said the suspected murder of Widdecombe had not been declared a terrorist incident at this stage, but confirmed that a counter terrorism investigation was underway alongside the murder inquiry.

Widdecombe, 78, was found dead at her home in Haytor, Devon, last Thursday. She had previously served as a Conservative MP and government minister before becoming a spokeswoman for Reform UK.

A 28-year-old white British man from Rotherham, South Yorkshire, was arrested on suspicion of murder on Saturday. He was later re-arrested on suspicion of the commission, preparation or instigation of acts of terrorism.

Taylor said detectives had been granted additional time to question the suspect, who can be held for up to seven days without charge under the warrant currently in place. Further extensions would require additional legal approval.

“The suspected murder of Ann Widdecombe has not been declared a terrorist incident,” Taylor said, adding that the counter terrorism investigation was “running in parallel” with the murder inquiry.

Police are examining a number of lines of inquiry, including Widdecombe’s public appearances on the day of her death. Taylor confirmed that her interview on TalkTV that morning was being reviewed as part of the investigation.

“We are exploring all lines of inquiry and that is one of the lines of inquiry that we’ll be exploring,” he said.

Home Secretary Shabana Mahmood said the suspect was not previously known to the government’s Prevent anti-extremism programme.

Police have also defended their initial handling of the investigation after criticism of the response following Widdecombe’s death.

Former prime minister Boris Johnson described the circumstances surrounding her death as “appalling and unforgivable”, while paying tribute to her as an “extraordinary politician”.