Police have named the suspect in the killing of Conservative MP Sir David Amess as Ali Harbi Ali.
The 25-year-old is a Briton of Somali heritage and is being held in custody under the Terrorism Act.
It is reported that Ali was known to counterterrorist police and had been referred to the government deradicalisation programme, Prevent.
Police are not looking for anyone else over the attack.
His father Harbi Ali Kullane, a former adviser to the prime minister of Somalia, told The Times of his shock at his son's arrest.
"I'm feeling very traumatised. It's not something that I expected or even dreamt of," he said.
Sir David Amess was MP for Southend West and died on Friday after being stabbed multiple times inside Belfairs Methodist Church in Leigh-on-Sea, in Essex.
The attack happened during a regular constituency surgery, prompting Home Secretary Priti Patel to order an urgent review of MPs' safety.
Police said on Friday that it was possible the attack was motivated by Islamic extremism.
Sir David was a committed Catholic and involved in the pro-life movement.
Church leaders and parliamentary colleagues alike have spoken of their sorrow over his death.
A vigil was held at St Peter's Roman Catholic Church, Leigh-on-Sea, on Friday evening, followed by a candlelit vigil in the town on Saturday night.
Patel joined with Prime Minister Boris Johnson, leader of the opposition Sir Keir Starmer and Commons Speaker Sir Lindsay Hoyle in visiting the scene of the attack where they laid flowers.
Speaking during her visit, Patel said, "We will carry on, we live in an open society, a democracy.
"We cannot be cowed by any individual or any motivation... to stop us from functioning, to serve our elected democracy."