The men suspected of the attacks in Woolwich were known by security services to hold extreme views, but until yesterday they were not thought capable of staging a terrorist attack.
A key part of the investigation now will be to find out how the two suspects were radicalised and whether they acted alone.
Alexander Hitchens, from the International Centre for the Study of Radicalisation, said such lone extremists believe there is "a war on their religion and it is their religious duty to respond in kind."
But the incident prompted a backlash from far-right activists who responded with attacks on mosques and anti-Islam demonstrations.
This report is by ITV News correspondent Juliet Bremner: