The Home Secretary has said politicians will not be “cowed” following the fatal stabbing of MP Sir David Amess, which police believe may be linked to Islamist extremism.

Priti Patel visited the scene at Belfairs Methodist Church in Leigh-on-Sea on Saturday morning alongside Prime Minister Boris Johnson, Labour leader Sir Keir Starmer and Commons Speaker Sir Lindsay Hoyle to pay their respects to Sir David, less than 24 hours after he was killed at a constituency surgery.

Ms Patel said security measures were being put in place to protect MPs but vowed they will carry on serving the country unimpeded in the face of the attack, which the Metropolitan Police have declared was a terrorist incident.

Speaking at Southend Police Station, the Home Secretary said: “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 democracy.”

Asked whether there could be a balance between the safety of MPs and the democratic process, she said: “It can be balanced, it can absolutely be balanced.”

Ms Patel said Sir David was “was killed doing a job that he loves, serving his own constituents as an elected democratic member and, of course, acts of this… are absolutely wrong, and we cannot let that get in the way of our functioning democracy.”

“So that is why there are measures under way right now – I convened meetings yesterday, I’ve been with the Speaker of the House, and with the police and our security services to make sure that all measures are being put in place for the security of MPs so that they can carry on with their duties as elected democratic members,” she added.

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 was later further detained under section 41 of the Terrorism Act 2000 and is in custody at a London police station.

A warrant of further detention, which allows detectives to hold the man until October 22, was granted at Westminster Magistrates’ Court on Saturday.

The name the police have for the suspect is Ali Harbi Ali, the PA news agency understands.

Official sources told PA the man is believed to be a British national with Somali heritage.

The investigation is assuming there was an Islamist extremist motivation for the attack, official sources said.

But it is understood the suspect was not, and had not previously been, a subject of interest for the security services.

According to reports, some sources have claimed the suspect has the same details as a man previously referred to Prevent, the anti-terror programme for those thought at risk of radicalisation. But there is yet to be any official confirmation of whether this is the case.

As part of the investigation, officers were carrying out searches at three addresses in the London area, the Met Police said. One search has now concluded.

A post-mortem examination took place on Saturday, police said, but its findings have not yet been released.

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”.

Politicians put on a united front at the church on Saturday morning, with Mr Johnson and Sir Keir individually laying flowers outside the building.

But MPs have raised concerns over their safety at constituency surgeries following the attack, sparking a debate over whether they should continue in person.

Veteran Labour MP Harriet Harman said she will be writing to the Prime Minister asking him to back a Speaker’s Conference to review the safety of parliamentarians.

Tory MP Tobias Ellwood, who was hailed as a hero for his attempts to save the life of Pc Keith Palmer during the Westminster terror attack in 2017, said face-to-face meetings with MPs should be paused until a security review has been completed.

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 told the PA news agency he dashed to the church when he heard Sir David had been “stabbed multiple times”.

He said: “David was there holding his surgery at that Methodist church and this person had gone there to join the surgery and when he got the chance and he went in to be seen by David, then he drew a knife and stabbed him.”

By the time Mr Lamb arrived, police cordons were up and he could not get into the church.

He said: “We knew it must be very serious because the paramedics had been working on Sir David for over two-and-a-half hours and they hadn’t got him on the way to hospital. We knew it had to be extremely serious and that the worst scenario could occur – we were hoping it wouldn’t but it did. That was when we heard that he had died.”

The Conservative councillor said a worker from Sir David’s office who was in the surgery during the attack was “not in touch at the moment because it’s so distressing, she’s getting counselling at the moment”.

Mr Lamb previously told the Daily Mail that 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.