The Metropolitan Police said it was possible the attack was linked to an extremist group.
A 25-year-old British man was arrested at the scene on suspicion of murder, and police say they are not looking for anyone else in Amess’ death.
According to police, as part of the investigation, officers conducted a search at two addresses in the London area.
Police forces believe the man acted alone, but investigations into the circumstances of the incident are continuing.
The man is being held in Essex. Government sources told BBC, Saturday (16/10/2021), that he is a British citizen who, from initial investigations, appears to be of Somali descent.
Sir David Amess, 69, who represents Southend West, was meeting in his constituency at the Belfairs Methodist Church on Friday when he was attacked at 00.05 am local time.
Essex Police Chief Constable BJ Harrington said: “Sir David was only doing his job when his life was horribly cut short”.