Counter-terrorism police have taken over the investigation into the killing of the Conservative MP David Amess, who died after being stabbed several times at an open advice surgery for his constituents in Essex.

The death of the 69-year-old veteran backbencher brought heartfelt tributes from all parties. Just five years after the murder of Jo Cox, it also prompted renewed worries about the security risks for MPs in an increasingly rancorous and polarised political era.

A 25-year-old man in custody has been arrested on suspicion of murder. Sources have told the Guardian he has the same details as someone who had previously been referred to the Prevent scheme, the official programme for those thought at risk of radicalisation. Police are not looking for anyone else.

Essex police briefed counter-terrorism policing headquarters about details of the attack and suspect throughout Friday afternoon. MI5, the domestic Security Service, was also monitoring the investigation.

Amess, who had represented Southend West since 1997, and had previously been the MP for the nearby Essex seat of Basildon from 1983, was stabbed several times at the constituency event at a church in Leigh-on-Sea late on Friday morning.

Paramedics treated Amess at the scene, but were unable to save his life.

In a statement to the media outside Southend police station, the chief constable of Essex, Ben-Julian Harrington, said police and paramedics arrived at the scene “within minutes” of being called.

“When they arrived, they found Sir David Amess MP, who had suffered multiple injuries. This was a difficult incident, but our officers and paramedics worked extremely hard to save Sir David. Tragically, he died at the scene.”

Harrington confirmed the investigation was being led by specialist counter-terrorism officers, adding: “It will be for investigators to determine whether or not this is a terrorist incident, but as always they will keep an open mind.”

News of the attack prompted shock and revulsion both in the constituency, where Amess was a well-known and visible figure, and from other MPs, faith leaders and others. Flags were flown at half-mast at Downing Street and parliament.

Priti Patel has ordered an immediate review of MPs’ security. A spokesman said: “The home secretary has asked all police forces to review security arrangements for MPs with immediate effect and will provide updates in due course.”

The Commons Speaker, Lindsay Hoyle, said the killing would “send shock waves across the parliamentary community and the whole country”, adding: “In the coming days we will need to discuss and examine MPs’ security and any measures to be taken.”

John Lamb, Conservative councillor for the neighbouring ward of West Leigh and a former leader of the council, said Amess would hold his advice surgeries in a range of locations because “he wanted to come out and about and meet people”.

Lamb said he had learned of the attack from a party colleague, who had been in touch with people who were with Amess at the church. “They phoned her up to say: ‘David’s been stabbed several times,'” Lamb said. “I came straight over.”

Kevin Buck, the councillor for Prittlewell ward and a friend of Amess, said the MP’s assistant and PA were both with him when he was attacked, adding: “I would imagine they are traumatised, because they would have seen the whole thing.”

As news of the attack emerged, there were desperate hopes that the MP’s life could be saved, with an air ambulance sent to the scene. But just over two hours later, police released an updated statement saying the man attacked had died, subsequently confirming this was Amess.

Tributes flooded in from MPs across the political spectrum, many of them highlighting Amess’s 38-year career in the Commons, one spent entirely on the backbenches, as a champion of causes including animal rights and better treatment for endometriosis.

In a brief TV interview, Boris Johnson said he was “deeply shocked and heart-stricken” at the news. The prime minister said: “Above all, he was one of the kindest, nicest and most gentle people in politics. And he also had an outstanding record of passing laws to help the most vulnerable.

“We’ve lost today a fine public servant, and a much-loved friend and colleague, and our thoughts are very much today with his wife, his children and his family.”

Keir Starmer, the Labour leader, called it “a dark and shocking day”, adding: “The whole country will feel it acutely, perhaps the more so because we have, heartbreakingly, been here before.”

It was in 2016, shortly before the Brexit referendum, when Cox, a Labour MP, was killed shortly before holding a surgery in her constituency, raising worries about the safety of MPs and the extent of threats and other intimidation many receive on a routine basis.

Brendan Cox, her widower, tweeted: “Attacking our elected representatives is an attack on democracy itself. There is no excuse, no justification. It is as cowardly as it gets.”

Kim Leadbeater, Cox’s sister, who was elected as an MP for the same seat of Batley and Spen in West Yorkshire in July, said the news had left her “scared and frightened”. She said: “My phone started going straight away, my mum and dad, my partner, my friends – ‘Are you OK?’ – and I was OK, I was visiting a school. But the shock and the feelings for us as a family, obviously what we went through and another family are going through that again, it’s horrific.”

In 2010, another Labour MP, Stephen Timms, was stabbed twice at a constituency surgery by a student radicalised by online videos. In 2000, Andrew Pennington, an assistant to the Liberal Democrat MP Nigel Jones, was stabbed to death as he tried to protect Jones from an attacker who stormed his constituency office armed with a sword.