The British counterterrorism police on Tuesday said that Ann Widdecombe, a right-wing politician who was killed last week, had been the victim of a “targeted attack.”

Ms. Widdecombe, 78, was found dead at her home in Haytor, in Devon, southwestern England, on Thursday, having sustained serious injuries.

A 28-year-old white British man from Rotherham, a town in northern England around 270 miles away from the crime scene, was arrested on suspicion of murder on Saturday. On Monday, the police said that they were also holding him “on suspicion of commission, preparation or instigation of acts of terrorism.”

In a briefing to the news media on Tuesday, Assistant Commissioner Laurence Taylor, head of British counterterrorism policing, said that the 28-year-old man could be held for a total of seven days before being released or charged.

“It is clear that this was a targeted attack,” the assistant commissioner said, noting that officers were “working to understand the extent of any planning or preparation and the motivation that sits behind that attack,” without giving further details.

Ms. Widdecombe served as a minister in the Conservative government of Prime Minister John Major in the 1990s. More recently, she had become a prominent member of Reform U.K., the populist right-wing party led by Nigel Farage, a pro-Brexit campaigner.

Some Reform officials have criticized the police’s handling of the investigation. The Devon and Cornwall police force initially said they had no information to suggest the attack had been politically motivated, even after it emerged that the arrested man appeared to have driven a long distance to Ms. Widdecombe’s home.

On Tuesday, Alison Hernandez, the elected police commissioner for Devon and Cornwall, whose role is to hold the force to account, acknowledged the criticism but defended officers’ actions.

“It is not unusual that in a fast-paced investigation, more information comes to light that changes the nature or the character of what the police are dealing with,” she said in a statement.

Assistant Commissioner Taylor said that “extensive searches” had taken place at the address in Rotherham where the 28-year-old suspect had been arrested and that “digital forensic examinations” were also in progress.

However, he noted that the attack had not been declared a terrorist incident at this stage.

Describing the case as complex, he said that one line of investigation was whether other politicians linked to the Reform party had been targeted.

Ms. Widdecombe’s killing has increased concerns about the safety of British politicians in an era when many suffer online abuse and threats. During the past decade, two British lawmakers have been murdered: Jo Cox, of the Labour Party, in 2016, and David Amess, a Conservative, in 2021. Ms. Cox was killed by a white supremacist, and Mr. Amess by an Islamic State sympathizer.

Ms. Widdecombe was no longer a member of Parliament but she spoke regularly to the media on behalf of Reform, including in the days before her killing. Asked whether her TV appearances might have been linked to the attack, Assistant Commissioner Taylor said that was one of the lines of investigation.

On Monday, the home secretary, Shabana Mahmood, offered Mr. Farage a meeting with the head of an independent committee within the Home Office that manages security for prominent people in public life. In a statement on social media, Mr. Farage thanked Ms. Mahmood and said he would accept the meeting and would “discuss the security of all Reform politicians.”