Ann 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 also said he did not want to rule anything out 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.”