Yet Nick Raynsford, a member of Parliament, told CNN that the victim is believed to be a serving soldier who was based at a nearby barracks.
The soldier had apparently been on duty in central London and was returning to the Royal Artillery Barracks in Woolwich when he was attacked, Raynsford said.
The MP described Woolwich as a mixed, multicultural area, adding that troops stationed at the centuries-old military barracks there have a close relationship with locals.
Even as they worked to piece together what happened and why, British authorities beefed up security around Woolwich and all military barracks in London, according to a British government source.
And British Defense Secretary Philip Hammond said the killing was a "very shocking incident" and that the United Kingdom takes the safety of its troops "very seriously," as he headed into Wednesday night to a meeting of the country's civil emergency committee known as COBRA.
The incident raised concerns it may inflame animosity against Muslims, with Metropolitan Police deploying riot police as a precautionary measure. The Muslim Council of Britain, after condemning what it called "a truly barbaric act that has no basis in Islam," urged Muslims and non-Muslims alike "to come together in solidarity to ensure the forces of hatred do not prevail."
Later Wednesday, a man with two knives threw a smoke grenade into a mosque in Essex, a county east of London, and demanded someone come outside to answer to the Woolwich slaying, the mosque's secretary said. The only person inside called police who came quickly and arrested the man, said Al Falah Braintree Islamic Center secretary Sikander Sleemy.
"I believe this was a revenge attack for what happened in Woolwich," Sleemy said. "We strongly condemn what happened in Woolwich. It's not an Islamic act."
That attack had already spurred swift condemnations around the world and especially in Britain -- from a "concerned" Queen Elizabeth II, to London Mayor Boris Johnson's description of a "sickening and unforgivable act of violence," to Labour Party leader Ed Miliband's prediction that the "whole country will be horrified."
That's certainly true for Lauren Collins, who saw the gore up close.
"I still am quite shaken at what I've seen," she told CNN. "I've seen a victim of an awful attack, and I've seen a body of a young man."