The 25-year-old, who is a British citizen, with Somali heritage, is not thought to have been previously known to the security services.
However, the investigation into the killing of Sir David Amess is still in its infancy so that could change if new details emerge.
The suspect was arrested on Friday at the scene of the attack at a Methodist church in Leigh-on-Sea, Essex, where Sir David, MP for Southend West, had been holding his weekly constituency surgery.
The detained man was previously known to the government’s Prevent scheme, which is a programme to stop radicalisation, a Whitehall source said. This detail was first revealed by the Guardian newspaper, which said that his involvement was short.
He is still in custody following his arrest. The investigation into the attack is being led by Scotland Yard’s Counter Terrorism Policing.