LONDON — Two men accused of butchering a British soldier had been investigated previously by security services, a British official said Thursday, as investigators searched several locations and tried to determine whether the men were part of a wider plot to instill terror on the streets of London.

The men, suspected of hacking the off-duty soldier to death while horrified bystanders watched, boasted of their exploits and warned of more violence in images recorded on witnesses’ mobile phones. Holding bloody knives and a meat cleaver, they waited for the arrival of police, who shot them in the legs, according to a passerby who tried to save the dying soldier.

Prime Minister David Cameron vowed that Britain would not be cowed by the horrific violence, and that it would reject “the poisonous narrative of extremism on which this violence feeds.” Indeed, there were few signs of alarm in the British capital, which has been hit by terrorist attacks during a long confrontation with the Irish Republican Army and more recently by al-Qaida-inspired attacks.

“It’s hateful, it’s horrific and upsetting. But it doesn’t seem to have made much of a difference,” Christian White, 43, said at King’s Cross station, close to the site of a subway bomb in July 2005. “Londoners are used to living in a city where life is complicated.”

Even so, security was increased at military barracks and installations in the capital, with extra armed guards added in many cases. Police said extra patrols were added at sensitive areas, including places of worship, transport hubs and congested areas.

Wednesday’s attack took place near a military barracks in the Woolwich area of south London.