Britain's interior minister on Sunday said security for Members of Parliament (MP) would be beefed up, after a lawmaker was stabbed to death as he held a public meeting with constituents, in the second such attack in five years.

Veteran Conservative MP David Amess, 69, was talking with voters at a church in the small town of Leigh-on-Sea, east of London, when he was killed on Friday.

The attack has spread fear among MPs, coming just over five years after the similar killing of Labour MP Jo Cox in the febrile run-up to the Brexit referendum.

Police have said they are investigating "a potential motivation linked to Islamist extremism". The investigation is being led by Scotland Yard's Counter Terrorism Command.

Home Secretary Priti Patel has ordered a review of security measures for lawmakers and told Sky News that "we need to close any gaps" in security provision for MPs, whose work includes regular meetings with constituents, called "surgeries".

She said police and parliamentary authorities were implementing "immediate changes and measures that are actively being put in place, and discussed with MPs".

This includes MPs sharing information on their whereabouts with police. Close protection at surgeries was also "in consideration right now", she added.

The Sunday Telegraph reported that uniformed police were guarding some surgeries following the attack, which prompted calls from some MPs for a pause in face-to-face meetings.

Police said late on Saturday that detectives had until Friday to question the suspected attacker after he was detained under the Terrorism Act, which allowed them to extend his detention.

He has not been charged.

British media, citing unnamed official sources, identified the suspect as Ali Harbi Ali.

Reports said he was a British national of Somali descent who had been referred to Prevent, the UK's official counter-terrorist scheme for those thought to be at risk of radicalisation.

Ali is believed not have spent long on the programme, which is voluntary, and was never formally a "subject of interest" to MI5, the domestic security agency, said the BBC.

The Prevent programme is currently under independent review.

"We want to ensure it [the Prevent programme] is fit for purpose, robust, doing the right thing, but importantly, learning lessons," Patel told Sky News.

Detectives said they have been carrying out searches at three addresses in the London area in a "fast-paced investigation".

Police and security services believe the suspected attacker acted alone and was "self-radicalised", The Sunday Times reported, while adding he may have been inspired by Al-Shabaab, al-Qaida-linked Islamists in Somalia.

Ali's father, named as Harbi Ali Kullane and said to be a former adviser to the prime minister of Somalia, confirmed to The Sunday Times that his son was in custody, adding: "I'm feeling very traumatised."

Patel nevertheless stressed to the BBC: "We have the best security and intelligence agencies in the world."

The government stepped up security for MPs following the 2016 murder of Labour MP Jo Cox, 41, who was shot and stabbed outside her constituency meeting near Leeds, northern England.

House of Commons Speaker Lindsay Hoyle in The Observer wrote that "we need to take stock" and review whether security measures introduced after Cox's murder are "adequate to safeguard members, staff and constituents, especially during surgeries".

Tobias Ellwood, a Conservative MP who tried to save a stabbed police officer during a 2017 terror attack near the Houses of Parliament, on Saturday urged a temporary pause in face-to-face meetings with constituents, until the security review is complete.