The suspect held on suspicion of murdering Ann Widdecombe continues to be questioned by police.
The former Conservative minister, later a Reform UK spokesperson and Brexit Party MEP, was found dead at her home in Haytor on Dartmoor, Devon, on Thursday.
Counterterrorism police are now leading the investigation into her death after new evidence came to light.
A 28-year-old white British man who was arrested on suspicion of Widdecombe’s murder on Saturday has since been rearrested on suspicion of the commission, preparation or instigation of acts of terrorism.
Police could be allowed to hold him for up to 14 days for questioning under terrorism legislation if needed.
But Downing Street stressed the importance of protecting the “integrity” of the investigation.
Asked about the level of speculation around the case, the prime minister’s official spokesperson said on Monday: “I think the police have been very clear – haven’t they? – that this is a live murder investigation, and we would just echo that it’s important that the integrity of this investigation is protected and supported as they carry out this work.
“And of course, we would urge anyone with information to come forward to the police.”
Why has the suspect not been named?
Police forces and the Crown Prosecution Service do not make the names of suspects public unless they are charged with an offence.
This also means the press can usually only identify them if they have been charged.
This is the result of a 2022 judgment by the UK’s Supreme Court, which found an individual facing a criminal investigation has the right to remain unnamed by the media until charges are filed, as they have a reasonable expectation of privacy.
If charges are brought against an individual, the authorities tend to release their name, street address and age.
Those details comprise their legal identity and help prevent those who may share that name being wrongly identified in connection with a crime.
What the media can and cannot report at this time
Once an arrest is made, criminal proceedings become “active”.
At this point, media outlets are restricted in what they can report to avoid committing contempt of court. This ensures that any potential criminal trial would not be impacted by any reporting.
It means that media outlets cannot publish anything that creates a “substantial risk of serious prejudice or serious impediment to active proceedings”.
Following an arrest, the media are allowed to report a small number of factual details regarding the incident.
These can include the suspect’s age, gender, general location, the nature of the offence alleged, as well as the status of the investigation.
If the case is heard in court, the media can report what is said before a jury – unless certain reporting restrictions are in place.
Regarding this case, Laurence Taylor, the head of UK counterterrorism policing, said: “Building on the progress made by our colleagues in Devon and Cornwall Police, we now have new information and evidence that means Counter Terrorism Policing is now leading the investigation.
“We are pursuing multiple lines of inquiry 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.
“We would like to thank local communities, the wider public and the media for their ongoing support and patience, and would ask them to continue to support us in the next stage of the investigation.”