Police said a 25-year-old man was apprehended on suspicion of killing after the onslaught at a church in Leigh-on-Sea.
According to them they retrieved a knife and were not looking for anyone else linked with the incident.
Sir David, 69, had been an MP from the year 1983 and was married with five children.
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Obituary: Sir David Amess
Sajid Javid, Health Secretary said he was
“a great man, a great friend, and a great MP, killed while fulfilling his democratic role”.
Chancellor Rishi Sunak also said: “The worst aspect of violence is its inhumanity. It steals joy from the world and can take from us that which we love the most.
“Today it took a father, a husband, and a respected colleague. All my thoughts and prayers are with Sir David’s loved ones.”
Sir David, who appeared for Southend West, was holding a constituency surgery – where voters can meet their MP and discuss anxieties – at Belfairs Methodist Church in Eastwood Road North.
Essex Police said they were informed about a stabbing soon after 12:05 BST and found a man wounded.
He was attended to by emergency services but died at the scene.
Sir David was the second sitting MP to be murderd in the last five years, following the murder of Labour MP Jo Cox in 2016.
She was murdered outside a library in Birstall, West Yorkshire, where she was about to hold a constituency surgery.
Southend councilor John Lamb told the BBC that Sir David transferred his surgeries to different place around the constituency “to meet the people” and declared the attack was “absolutely dreadful”.
“We’ve lost a very good, hard working constituency MP who worked for everyone,” he said.
“It didn’t matter who you were, it didn’t matter about your religion or your culture. If you had a problem he would work for you.”
Political dispute have been set aside; MPs are united in showing their shock, sorrow and affection for a colleague and a friend.
Most of them will themselves have spent the day in church halls, supermarkets and high streets doing exactly what Sir David Amess had been: meeting their constituents eye-ball-to eye-ball.
When you talk to MPs, they’ll often tell you that it’s a very important part of the job and one they really appreciate.
The death of Sir David Amess is both a personal calamity – and a dreadful prompting of the very real risks they all face.
Sir Lindsay Hoyle, Speaker of the House of Commons said:
“This is an incident that will send shockwaves across the parliamentary community and the whole country.”
He declared that he was shocked and extremely saddened by the killing of a “lovely man”, and that in the coming days they would need to examine MPs’ security.
Sadiq Khan Labour London Mayor said he was
“deeply, deeply saddened” and described Sir David as “a great public servant”.
Sir Ed Davey Liberal Democrat leader said it was
“a truly terrible day for British politics but most importantly of all our prayers are with all the people who loved David”.
Who really was Sir David Amess?
A Conservative backbencher for about forty years, Sir David set foot in Parliament in 1983 as the MP for Basildon.
He held the seat in 1992, but divert to nearby Southend West at the 1997 election.
Raised as a Roman Catholic, he was known politically as a social conservative and as a prominent crusader against abortion and on animal welfare matters.
He was also known for promoting of Southend, in addition to a long-running crusade to win city status for the town.