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.
Prime Minister Boris Johnson said “our hearts are full of shock and sadness” at the loss of “one of the kindest” people in politics.
Sir David, 69, had been an MP since 1983 and was married with five children.
The investigation will be led by the Metropolitan Police’s specialist Counter Terrorism Command, who will determine whether it was a terrorist incident.