Counter-terrorism officers are conducting round-the-clock investigations into the background, travel history, telephone records and known associates of the two suspects in the Woolwich attacks to determine whether they had affiliations with al-Qaida or were lone wolves unconnected with any terrorist organisation.
The suspects, who have yet to be named, are being held under armed guard in hospital after they were shot by police at the scene following the gruesome murder of a soldier yesterday.
According to eyewitness accounts, two men rammed their car into a pedestrian, believed to be a serving soldier, jumped out of the vehicle and butchered him on the street using knives and machetes in broad daylight.
Police have repeatedly warned of the difficulty of guarding against attacks by "clean skins" - assailants unknown to the authorities, who have not appeared on the radar of the security agencies, and who have no previous criminal background.
While the suspects may have sympathies with al-Qaida ideology, they may not have received any organisational or financial backing from the group. Video footage taken by witnesses in the immediate aftermath of the attack captured one of the suspects making pronouncements in line with the rhetoric of the organisation.
"We swear by almighty Allah we will never stop fighting you. This British soldier is an eye for an eye, a tooth for a tooth. We must fight them," the suspect said. "You people will never be safe. Remove your government. They don't care about you."
Another line of inquiry will be whether the killers were radicalised at a mosque or in prison, where an increasing number of youths are targeted by radical Islamist groups.
Difficult to protect against
John O'Connor, a former Flying Squad commander at Scotland Yard, said: "This has all the hallmarks of a very low-key terrorist incident which raises a number of problems for the authorities.
"This type of attack is very difficult to protect against because it is not as though you are talking about a network of people following their plans. This could spring up anywhere and that's the concern. It's very difficult to keep a tab on where this is going and where the threat level is.
"This is a departure from the established type of attacks that you see or the established plans that you see of terrorism causing mass murder. You're into a new round of terror threats in this country, particularly as you don't know the full extent of it. As you don't know that - and I don't suppose the authorities know that - they have got to look at the worst case scenario."
Former home secretary John Reid also warned of the difficulty of countering the lone wolf threat. "If it is a terrorist attack, if it is proven to be, it is very difficult to counter because people tend to think of terrorist attacks as being all organised from the centre, from the al-Qaida core," he said.
"But in fact one of the hardest things to counter - by the police, the intelligence services and others - the lone wolf-type attack, which may be inspired by al-Qaida but doesn't have the central planning. It's far more difficult to trace, its sometimes done with what's called 'clean skins' - people with no record."
Jonathan Evans, the former director general of MI5, warned last year of the threat from "lone actors", while the Royal United Services Institute (RUSI) thinktank published a report outlining the difficulties faced by the security agencies.
It stated: "Though the death of Bin Laden began a succession of counter-terrorist victories in 2011, the threat from jihadist terrorism has not diminished. If anything, the risk has evolved from plots carried out by organised cells within a leadership structure, to one carried out by lone wolves, radicalised by material on the internet.
"The latter is harder to track down and is potent given the uncertain international situation; where the outcome of the Arab Spring has not been settled, and where there are frequent returns of British citizens from war zones such as Somalia and Yemen."
RUSI director Michael Clarke said: "More experienced lone-wolf terrorists are likely to be returning to Britain in the next couple of years, not from training camps in Pakistan and via airports in Karachi and Dubai, but from wars in Somalia, Yemen, or Nigeria, from the renewed violence in Iraq, and from destinations and via routes that will be far more difficult for security services to monitor."
Jihadist destination of choice
Hundreds of Britons are known to have travelled to Syria over the last two years to support the rebellion against President Bashar al-Assad. Syria is now the "jihadist destination of choice", according to Whitehall officials, and while some individuals are known to security agencies, many others are not.
Britons are also known to have been involved with the al-Nusra front, a militant group in Syria with al-Qaida links, while others have been travelled to Somalia to fight alongside the al-Qaida affiliate al-Shabaab.
"What they do when they come back here is more worrying to us than what they do when they are out there," said one official.
Another possible motivating factor could be the online Islamist outlet Inspire, described as "al-Qaida's English-language magazine", and produced by al-Qaida in the Arabian Peninsula (Aqim).
It carries exhortations to groups and individuals urging them to carry out attacks and even carries instuctions on bomb-making techniques for so-called "self-starters" who have no previous contact with terror groups.
Inspire has been linked to at least 15 terrorism cases, including April's Boston Marathon bombings. One article was entitled "How to build a bomb in the kitchen of your mom".
Websites linked to Al Qaeda could be attracting up to 250,000 visits daily, say security officials.
Security has been tightened at all London barracks after Home Secretary Theresa May chaired a meeting of the government's emergency committee, Cobra, following the attack.
Security chiefs sitting on the Joint Terrorism Analysis Centre are reviewing the national threat level, which stands at level three on a scale of five, indicating a "substantial" threat.
The MoD issued directed military personnel to wear civilian clothes in "areas of tension" and not to carry military bags or T-shirts or anything that might compromise their security.
The security services and police have foiled more than a dozen terror plots in the UK since 2005, including planned attacks on airliners, shopping centres, nightclubs and the London Stock Exchange.
In 2010, Roshonara Choudhry was convicted of attempting to murder Labour MP Stephen Timms at his constituency office. In 2008, British Pakistani Parviz Khan and five associates were jailed for planning to kidnap a Muslim solder and film his execution.
Earlier this year three men were jailed for a plot to attack the town of Wootton Bassett in Wiltshire, where the the funerals of armed forced personal take place after their repatriation.