The killing of Conservative MP Sir David Amess is being treated as a terrorist incident by police.
Sir David was stabbed multiple times at his constituency surgery in Leigh-on-Sea in Essex on Friday.
The Metropolitan Police said there was a potential link to Islamist extremism. A 25-year-old British man was arrested at the scene on suspicion of murder.
Prime Minister Boris Johnson and Labour leader Sir Keir Starmer laid flowers at the scene together on Saturday morning.
Home Secretary Priti Patel and Commons Speaker Sir Lindsay Hoyle also paid their respects outside Belfairs Methodist Church in Leigh-on-Sea.
Speaking later, Ms Patel paid tribute to Sir David as a “man of the people”, saying “he was absolutely there for everyone” and was “killed doing a job he loved”.
“We are all struggling to come to terms with the fact that David Amess has been so cruelly taken away from all of us,” she said, adding: “All our thoughts right now are absolutely with David and David’s dear, dear family.”
The Met said officers are carrying out searches at two addresses in the London area and are not seeking anyone else over the death.
The force believes the man, who is in custody in Essex, acted alone but inquiries into the circumstances of the incident are continuing.
Government sources have told the BBC he is a British national who, from initial inquiries, appears to be of Somali heritage.
Sir David, 69, who represented Southend West, was holding a constituency surgery – where voters can meet their MP and discuss concerns – at the church on Friday when he was attacked at 12:05 BST.
Essex Police Chief Constable BJ Harrington said Sir David was “simply dispensing his duties when his life was horrifically cut short”.
Counter-terrorism officers are working with Essex Police and the Eastern Region Specialist Operations Unit.
“The fatal stabbing in Leigh-on-Sea has tonight been declared as a terrorist incident, with the investigation being led by Counter Terrorism Policing,” the Met said.
“The early investigation has revealed a potential motivation linked to Islamist extremism.”
Officers are appealing for anyone with any information or with footage from CCTV, dash cams or video doorbell, to contact them.
The home secretary has asked police forces to immediately review security arrangements for MPs, saying the killing represented “a senseless attack on democracy itself”.
Ms Patel added that “questions are rightly being asked about the safety of our country’s elected representatives”.
Sir David had been an MP since 1983 and was married with five children. He is the second serving MP to be killed in the past five years, following the murder of Labour MP Jo Cox in 2016.
Prime Minister Boris Johnson described him as “one of the kindest, nicest, most gentle people in politics”.