A 28-year-old man is suspected of murder and terrorist offences.
"It is clear that this was a targeted attack," said Laurence Taylor, head of the national counter-terrorism unit in the police, at a press conference.
We are continuing to work to understand the extent of any planning or preparation and the motivation behind the attack.
Ann Widdecombe, 78, was found dead in her home in southwest England on Thursday. Police believe she was attacked about a day before her body was found.
Widdecombe was, among other things, a Conservative minister in the Home Office and the Department of Employment from 1994 to 1997 under Prime Minister John Major.
