Boris Johnson and Sir Keir Starmer lay flowers at scene of Sir David Amess death
Mr Johnson was also accompanied by Commons Speaker Sir Lindsay Hoyle and Home Secretary Priti Patel.
They laid a wreath at the front of Belfairs Methodist Church in Leigh-on-Sea, where Sir David was killed on Friday.
It came after Scotland Yard said the country’s most senior counter-terror officer, Deputy Assistant Commissioner Dean Haydon, has formally declared the incident as terrorism and said early investigations have revealed “a potential motivation linked to Islamist extremism”.
Sir David, 69, who had been an MP since 1983, was fatally injured while meeting constituents.
A 25-year-old man arrested at the scene on suspicion of murder is in custody at an Essex police station.
As part of the investigation, officers are also carrying out searches at two addresses in the London area, the Met said.
Sir David’s death has prompted police forces to contact all MPs to discuss their security and personal safety.
Investigators believe Sir David’s killer acted alone and are not seeking anyone else in connection with his death.
According to reports, the knifeman was waiting among a group of people to see Sir David at the church and launched the attack shortly after the MP arrived.
Local councillor John Lamb, who arrived at the scene shortly after the incident, told the Daily Mail Sir David was with two female members of staff – one from his constituency office and one from his parliamentary office – when a man “literally got a knife out and just began stabbing him”.
Chief Constable of Essex Police Ben-Julian Harrington said Southend West MP Sir David was “simply dispensing his duties when his life was horrifically cut short”.
Tory veteran Sir David, who was described by Mr Johnson as “one of the kindest, nicest, most gentle people in politics” was married with five children.
The attack came five-and-a-half years after Labour MP Jo Cox was killed by a far-right extremist in her Batley and Spen constituency in West Yorkshire.
Home Secretary Priti Patel said a balance could be found between the democratic process and the security of MPs, adding that “we cannot be cowed by any individual or any motivation … to stop us from functioning.
“We are open to surgeries, doing our job. We will continue to do that.
“David was a dear friend of mine and a loyal friend and colleague, a man of the people. He was killed serving his own constituents and constituency members.
“We will carry on, we live in an open society, a democracy. We cannot be cowed by any individual or any motivation… to stop us from functioning, to serve our elected a democracy.”
A National Police Chiefs’ Council spokesman said every MP will be contacted by Operation Bridger, a nationwide police protective security operation established in 2016, to discuss their security arrangements following the death of Sir David Amess.
The spokesman said: “In light of yesterday’s tragic attack, every MP will be contacted individually by Op Bridger representatives in their local force to discuss their security arrangements.
“They will also speak to MPs about security arrangements for any events they are planning to attend in the coming days, so the appropriate advice can be provided"