Police are continuing to question the suspect held on suspicion of the murder of politician Ann Widdecombe for a third day.
A white British man, 28, from Rotherham, South Yorkshire, was originally arrested on suspicion of murder on Saturday, before being re-arrested on Monday on suspicion of commission, preparation or instigation of acts of terrorism.
Widdecombe, 78, a former Conservative minister turned Reform UK spokeswoman, was found dead at her home in Devon on Thursday, having sustained serious injuries.
From the time of his arrest for murder on Saturday, police would have had 96 hours to charge the suspect.
However someone arrested under the Terrorism Act can be held for up to two weeks without charge.
On Monday, it was confirmed that Counter Terrorism Policing was leading the investigation into Widdecombe's death, after Devon and Cornwall Police initially said there was "nothing to suggest" the murder had been politically motivated.
Counter Terrorism Policing South East (CTPSE) said it had taken over the investigation after new information had "come to light".
National Counter Terrorism Policing head Laurence Taylor said the new arrest built on "progress made by our colleagues in Devon and Cornwall Police", and that they were working to establish "the motivation for this attack".
"Our priority is progressing this investigation quickly, with all the capabilities we have available to us. If anyone has any information, please share it with the police," he said.
The announcement comes after the suspect was seen in CCTV footage appearing to get into a car in Yorkshire just before 08:00 BST on Wednesday morning, hours before the former Conservative minister is thought to have been attacked in her home in Devon.
Devon and Cornwall Police said they believed Widdecombe had been attacked on Wednesday at about 12:30.
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Speaking in the House of Commons on Monday, Home Secretary Shabana Mahmood confirmed the suspect was not known to the government's Prevent anti-terror scheme.
She said her death raised questions about the security of those in public life, and that police intended to issue guidance to MPs on safety soon.
Widdecombe served as the Conservative MP for Maidstone for 23 years, holding ministerial roles in Sir John Major's government between 1994 and 1997.
Following her departure from the Commons in 2010, Widdecombe appeared on the BBC's Strictly Come Dancing that year, and was a runner-up on Celebrity Big Brother eight years later.
She joined the Brexit Party in 2019, where she represented South West England as its MEP from 2019 to 2020.
