They did confirm that the victim was a serving British soldier. His family has asked that his name not be immediately released.
After the killing, one of the attackers was recorded on numerous amateur videos making threats, explaining the reason for the crime, and shouting political slogans while gesturing with bloodied hands and waving a meat cleaver.
"We swear by almighty Allah we will never stop fighting you," the man declared, complaining about British troops fighting Muslims. "We must fight them as they fight us."
The camera then panned away to show a body lying on the ground. This video, with its venomous threats, may provide the lasting image of the tragedy.
A British government official said both suspects were part of previous security services investigations for possible terror links.
The official, who spoke on condition of anonymity because he was not authorized to speak about the investigation, said he could not provide other details because the suspects may face trial. Investigations by Britain's domestic security service, MI5, can include undercover surveillance, phone tapping and communications intercepts.
Police in the county of Lincolnshire in eastern England said a property was being searched in connection to the attack in Woolwich. Police said a search warrant had been obtained but would not provide details about the search. Police were also scouring the attack site for further clues.
The incident unfolded Wednesday afternoon when officers responded to reports of an assault just a few blocks from the Royal Artillery Barracks in Woolwich.
Fred Oyat, 44, who lives in a high-rise nearby, said he heard four gunshots and 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."