(BBC) Police said a 25-year-old man was arrested on suspicion of murder after the attack at a church in Leigh-on-Sea.
They said they recovered a knife and were not looking for anyone else in connection with the incident.
Sir David, 69, had been an MP since 1983 and was married with five children.
Health Secretary Sajid Javid said he was “a great man, a great friend, and a great MP, killed while fulfilling his democratic role”.
Chancellor Rishi Sunak said: “The worst aspect of violence is its inhumanity. It steals joy from the world and can take from us that which we love the most.
“Today it took a father, a husband, and a respected colleague. All my thoughts and prayers are with Sir David’s loved ones.”