Officers are looking for a suspect, who they believe to be a white male, in connection with the case, which they say is “moving at a significant pace”.
In a statement they said they would like to hear from “anyone who may have seen anything suspicious in the vicinity of Haytor Vale, Haytor, or anyone with CCTV, doorbell or dashcam footage which could assist with our investigation”.
Extra uniformed officers will be in the area to help with enquires and to reassure residents, they added.
Det Ch Insp Ilona Rosson said: “This is an extremely tragic incident and our thoughts are very much with the family and friends of Ann Widdecombe at this difficult time
“I would appeal to anyone who may have information about this incident, however insignificant it may seem, to come forward and speak with us.”