Counter-terror police are investigating yesterday's attack in which two men hacked the soldier to death in broad daylight. They were shot and wounded by police and are now in hospitals under armed guard.
The gruesome nature of the murder - some witnesses say the men tried to decapitate their victim - their politically-fuelled rants to passers-by, and their apparent desire for publicity all point to militant Islamist extremism, experts say.
"This is a departure from the established type of attacks that you see or the established plan that you see of terrorism causing mass murder," explained John O'Connor, a former head of the Scotland Yard police headquarters' 'Flying Squad' detective unit.
Security experts have long warned of the risk of terror attacks from individuals who slip under the radar.
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Meanwhile, Prime Minister David Cameron has acknowledged reports that the two suspects may have been previously known to the intelligence services, but praised the work of the security forces in foiling plots up until now.
The murder was the first fatal Islamist attack in Britain since 52 people were killed in suicide bombings on the London transport system eight years ago.
Some of these have targeted British soldiers, who were once told not wear their uniforms in public due to a threat from Irish republicans, but in recent years have been encouraged to do so.