Detectives are continuing to question a 25-year-old British man who was detained at the scene of Friday’s fatal stabbing of MP Sir David Amess.
Officers spent Saturday searching two addresses in the London area band are not seeking anyone else.
Police are treating the attack in Essex as a terrorist incident, which may be linked to Islamist extremism.
Meanwhile, a candlelit vigil is under way in Leigh-on Sea, where the attack took place, to mark Sir David’s life.
The suspect, who has not been named, is being held on suspicion of murder at an Essex police station, where he will be facing questions from the Metropolitan Police’s counter terrorism team.
Police could potentially hold him until Tuesday before having to charge him, or let him go.
Government sources told the BBC that from initial inquiries, the UK national appeared to be of Somali heritage.
BBC security correspondent Frank Gardner said Whitehall officials were saying the arrested man was not on a database of terror suspects.
The UK’s threat level has not changed since Friday and remains at “substantial”, meaning a terror attack is likely.
Sir David, a Conservative MP since 1983, was holding one of his regular Friday meetings with his constituents at Belfairs Methodist Church when he was stabbed multiple times.
The 69-year-old was married with four daughters and a son. He is the second MP to be killed in recent years, following the murder of Labour MP Jo Cox in July 2016.
This latest attack has raised concerns for the safety of MPs, many of whom hold constituency surgeries which anyone can attend.
Home Secretary Priti Patel said security measures were being put in place to protect MPs – but insisted they would carry on serving the country unimpeded.
“We will carry on, we live in an open society, a democracy,” she said during a visit to the scene of the attack with Prime Minister Boris Johnson, Labour leader Sir Keir Starmer and Commons speaker Sir Lindsay Hoyle.
“We cannot be cowed by any individual or any motivation… to stop us from functioning, to serve our elected democracy.”
Ms Patel maintained a balance could be found to allow face-to-face meetings with constituents to continue.
However, Conservative MP Tobias Elwood – who came to the aid of a stabbed police officer during the 2017 terror attack in Westminster – suggested MPs speak to constituents on the phone or over Zoom for the time being.
Labour MP Diane Abbott said she would prefer to meet constituents behind a screen to prevent possible stab attacks.
And Kim Leadbeater, the sister of Mrs Cox, said her partner had asked her to stand down as MP for Batley and Spen after Sir David’s death.
