Prime Minister David Cameron held an emergency meeting of his intelligence chiefs to assess the response to what he called a "terrorist" attack; it was the first deadly strike in mainland Britain since local Islamists killed dozens in London in 2005.
"We will never give in to terror or terrorism in any of its forms," Cameron said outside his Downing Street office.
"This was not just an attack on Britain and on the British way of life, it was also a betrayal of Islam and of the Muslim communities who give so much to our country. There is nothing in Islam that justifies this truly dreadful act."
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He said there would be a review of how intelligence had been handled - Adebolajo had been known to authorities for handing out radical Islamist pamphlets in Woolwich.
One source close to the inquiry said the local backgrounds of the suspects in a multicultural metropolis - nearly 40 percent of Londoners were born abroad - and the simplicity of the attack made prevention difficult:
"Apart from being horribly barbaric, this was relatively straightforward to carry out," the source said. "This was quite low-tech and that is frankly pretty challenging."
Anjem Choudary, one of Britain's most recognised Islamist clerics, told Reuters Adebolajo, was known to fellow Muslims as Mujahid - a name meaning "warrior": "He used to attend a few demonstrations and activities that we used to have in the past."
He added that he had not seen him for about two years: "When I knew him he was very pleasant man," Choudary said. "He was peaceful, unassuming and I don't think there's any reason to think he would do anything violent."
A man called Paul Leech said on Twitter he had been at school in the east London suburb of Romford with the man seen claiming the attack: "Michael Adebolajo u make me sick," he wrote. "How could someone who was a laugh and nice bloke at school turn out like that. I'm ashamed to have known u."
The two men used a car to run down the young soldier, whose name was not made public, near Woolwich Barracks in southeast London and attempted to behead him with a meat cleaver and knives, witnesses said, before telling shocked bystanders they acted in revenge for British wars in Muslim countries.
A dramatic clip filmed by an onlooker showed one of the men, identified as Adebolajo, his hands covered in blood and speaking in a local accent apologising for taking his action in front of women but justifying it on religious grounds:
"We swear by almighty Allah we will never stop fighting you. The only reason we have done this is because Muslims are dying every day," he said. "This British soldier is an eye for an eye, a tooth for a tooth."
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The attack revived fears of "lone wolves". These may have had no direct contact with al Qaeda but are inspired by radical preachers and by Islamist militant Web sites, some of which urge people to attack Western targets with whatever means they have.
Images of the blood-soaked suspect - who urged Britons to overthrow their government or risk having their children face the fate of the dead soldier lying just yards away - were splashed across the front pages of newspapers; so too were links to his clearly spoken, matter-of-fact video statement, made as the pair chatted calmly to bystanders before police arrived.
In Nigeria, with a mixed Christian-Muslim population and where the authorities are battling an Islamist insurgency, a government source said there was no evidence the Woolwich suspects were linked to groups in west Africa.
The grisly attack took place next to the sprawling Royal Artillery Barracks in Woolwich, a south London working class district which has long-standing historic links to the military and is home to many immigrant communities, including Nigerians.
The victim was wearing a T-shirt saying "Help for Heroes", the name of a charity formed to help wounded British veterans. Britain has had troops deployed in Afghanistan since 2001 and had troops in Iraq from 2003-2009.
Witnesses said they shouted "Allahu akbar" - Arabic for God is greatest - while stabbing the victim and trying to behead him. A handgun was found at the scene.
Some onlookers rushed to help the victim and one woman tried to engage one of the attackers in conversation to calm him.
"He had what looked like butcher's tools — a little axe, to cut the bones, and two large knives. He said: 'Move off the body,'" Ingrid Loyau-Kennett was quoted as saying.
"He said: 'I killed him because he killed Muslims and I am fed up with people killing Muslims in Afghanistan.'"
A trained first aider and Cub Scout leader, Loyau-Kennett was on a bus which was held up by the incident and she got off to try to help the victim. She found he was already dead.
Her attitude and that of other passers-by who remonstrated with the attackers was held up by Cameron as an example of resistance to attempts to terrorise the population:
"When told by the attacker that he wanted to start a war in London," Cameron said, "She replied, 'You're going to lose. It's only you versus many.' She spoke for us all."
'Help for Heroes'
London was last hit by a serious militant attack on July 7, 2005, when four young British Islamists set off suicide bombs on underground trains and a bus, killing 52 people and wounding hundreds. A similar attack two weeks later was thwarted.
In 2007, two days after police defused two car bombs outside London nightclubs, two men suspected of involvement, a British-born doctor of Iraqi descent and an Indian-born engineer, rammed a car laden with gas into the Glasgow Airport terminal, setting it ablaze. One of the attackers died and the other was jailed.
Britain has long known political violence on the streets. In 2009, two British soldiers were shot dead outside a barracks in Northern Ireland in an attack claimed by Irish republicans.
Woolwich, too, has seen attacks before. A soldier and a civilian were killed by an IRA bomb at a local pub in 1974. The barracks itself was bombed in 1983, wounding five people.
Since the 2005 bombings, known as 7/7, security chiefs say they have faced at least one plan to carry out an attack on the level of those attacks and have warned that radicalised individuals posed a grave risk to national security.
Peter Clarke, who led the investigation into the 7/7 bombings, said that if the Woolwich attackers did turn out to be acting alone, it showed the difficulty the security services faced in trying to stop them.
"An attack like this doesn't need sophisticated fund raising and sophisticated communications or planning," he told Reuters. "It can be organised and then actually delivered in a moment."
The bombing attacks on the Boston Marathon last month, which U.S. authorities blame on two brothers, have raised the profile of the "lone wolf" threat in the West. A French-Algerian gunman killed three off-duty French soldiers and four Jewish civilians on a rampage in southern France last year.
Britain's involvement in the wars in Afghanistan and Iraq in the past decade has often stirred anger among British Muslims and occasionally made soldiers a target at home. British police have foiled at least two plots in which Islamist suspects were accused of planning to kill soldiers, including by beheading.
Cameron's office officials had welcomed the condemnation from most mainstream British Muslim groups but that the national security committee had discussed community cohesion.
In signs of a backlash after the attack, more than 100 angry supporters of the English Defence League, a far-right street protest group, took to the streets on Wednesday.
Separately, two men were arrested in connection with separate attacks on mosques outside London. No one was hurt.