Sir David, the MP for Southend West, died after he was stabbed more than 20 times during a constituency surgery in Leigh-on-Sea, Essex, on 15 October.
Officers were heard to shout “drop the knife” as they entered Belfairs Methodist Church after the attack.
Ali Harbi Ali, 26, denies charges of murder and preparing acts of terrorism.
The trial at the Old Bailey also heard how Mr Ali told police officers he had committed a “terror-related crime.
PCs Scott James and Ryan Curtis entered Belfairs Methodist Church armed only with a baton and incapacitant spray, the court was told, despite being warned the suspect had a knife.
PC Curtis told the jury they found Mr Ali standing in the aisle of the church with a blood-stained knife in his hand.
Body-worn footage from PC James was played to the court and showed the officer deciding against waiting for backup from a team with a Taser.
The footage showed them shouting “drop the knife!” on entering the church. After a short stand-off, the suspect dropped the weapon and officers handcuffed him.
In the aftermath of the arrest, Mr Ali, who was believed to be on the phone to his sister at the time said “My phone’s rung, it’s the family.
Shouting, he added: “Don’t worry. The police got me. They’re not gonna shoot.”
Mr Ali was on the video saying “I was prepared to die”, the court heard.
He was taken to Southend police station and asked if the crime might be domestic or hate-related.
Mr Ali told the booking officer: “Terror. Religious”, the jury heard.
Previously, jurors were played a 999 call from the aftermath of the attack where a witness said Mr Ali was threatening to kill four other people.
They were also shown CCTV images earlier in the trial showing how Mr Ali travelled from his Kentish Town, north London, home to Leigh-on-Sea on the day of the killing.
The trial previously heard how Mr Ali allegedly spent years researching a number of potential high-profile political targets including Michael Gove, Dominic Raab and Sir Keir Starmer.
