British officials said the attack appeared to be an act of terrorism, possibly motivated by radical Islam.
The two suspects remained hospitalized on Wednesday night but their identities and that of their victim were not known. One of them was reported to be in serious condition.
The afternoon attack occurred in the southeast London neighborhood of Woolwich, just a few blocks from the Royal Artillery Barracks.
In Paris, French President Francois Hollande, speaking at a press conference with British Prime Minister David Cameron, said the slain man was a British soldier. Cameron didn't immediately confirm that fact but the Britain's Ministry of Defense said it was urgently investigating if a U.K. soldier was involved.
Cameron said there were "strong indications" it was a terrorist incident.
"We have suffered these attacks before, we have always beaten them back," Cameron said. "We will not be cowed, we will never buckle."
One British broadcaster ran video footage of what appeared to be one of the attackers, his hands covered in blood, making political statements about "an eye for an eye" to an unknown cameraperson as a body lay behind him on the ground.
There was no immediate way for the Associated Press to verify who the cameraman was.
The footage — obtained by ITV news — showed a man in a dark jacket and knit cap walking toward a camera, clutching a meat cleaver and a knife in what appear to be bloodied hands. With a British accent, he apologized in English for the women passers-by who "have had to witness this" attack, saying that "in our land our women have to see the same."
He gave no indication what that land was.
"We must fight them as they fight us," the man told the camera as people milled around behind him. The camera then panned away to show a body behind the man.
The Associated Press examined the footage to verify its authenticity. The AP cross-referenced images from the scene, aerial shots, the location of a car behind the alleged attacker and appearance of a body and car in the background of the image.
The British Cabinet's emergency committee immediately called a meeting and the prime minister's office said security was stepped up at barracks across London. Cameron cut short his Paris trip to return to London and his office said he would chair another emergency committee meeting Thursday.
The barracks — which house a number of the King's Troop Royal Horse Artillery and independent companies of the Grenadier and Coldstream Guards — were the site of shooting events during the 2012 London Olympics.
Fred Oyat, a 44-year-old who lives in a high-rise near where the attack occurred, said he heard four gun shots and then went straight to the window.
"I saw one man lying there bleeding, another lying on the pavement being disarmed. A policeman was pointing a gun at him. A third man was lying further up the street ... he was bleeding profusely," Oyat said. "There were four knives on the ground — big kitchen knives. The knives were very bloody."
David Dixon, head teacher of a nearby primary school, saw a body lying in the road outside and said police told him there was a serious incident. He told the BBC he then made sure students were inside and put the school into a lockdown mode. He said he then heard shots fired.
The Independent Police Complaints Commission, which is called in when officers are involved in shootings, confirmed that it is investigating the attack.