Both suspects in the killing of a serving soldier in London were known to security services, senior Whitehall sources have confirmed to the BBC.
One of the suspects is understood to be 28-year-old Muslim convert Michael Adebolajo, according to sources.
He and another man are under arrest in hospital after being shot by police after Wednesday's attack in Woolwich.
Prime Minister David Cameron has said the UK will "never give in to terror or terrorism".
Shortly after the killing a man, thought to be Mr Adebolajo, was filmed by a passer-by, saying he carried out the attack because British soldiers killed Muslims every day.
Sources said reports the men had featured in "several investigations" in recent years - but were not deemed to be planning an attack - "were not inaccurate".
They confirmed one of the suspects was intercepted by police last year while leaving the country.
Speaking outside 10 Downing Street on Thursday, Mr Cameron said: "One of the best ways of defeating terrorism is to go about our normal lives."
He said there was no justification in Islam for the attacks, which were "solely and purely" the responsibility of the individuals involved.
Across London there are 1,200 extra police officers on duty in response to the attacks, Assistant Commissioner Simon Byrne said.
Earlier officers raided a flat believed to belong to one of the attackers on a Greenwich housing estate.
Neighbours said two sisters in their 30s, an older woman and a teenage boy were taken away in a police van.
An address in Saxilby, Lincolnshire, is also being searched in connection with the attack.
According to BBC sources, Mr Adebolajo, a Briton of Nigerian descent, comes from a devout Christian family but took up Islam after leaving college in 2001.
He was described as "bright and witty" when he was at college.
Witnesses said the soldier was attacked at 14:20 BST with knives and a cleaver in Artillery Place, near Woolwich Barracks, by two men shouting Allahu Akbar (God is Great).
The men made no attempt to flee and encouraged people to take pictures of them and the victim.
In footage obtained by ITV News, one of the men was filmed wielding a bloodied meat cleaver and making political statements.
"You think politicians are going to die?," he said. "No, it's going to be the average guy - like you - and your children.
"So get rid of them. Tell them to bring our troops back so you can all live in peace."
Another eyewitness said the police "didn't even get a chance to get out of their car".
"They just had to shoot him because he was just hurtling towards them," Graham Wilders told the BBC. "And then the other one, with the handgun, lifted it up and obviously they shot him."
In other developments:
- The Metropolitan Police says police officers arrived within nine minutes of the first 999 call and armed officers were there within 14 minutes
- Another cabinet emergency meeting is likely to be held on Friday, sources said
- An increased police presence will be in Woolwich and the surrounding areas through Thursday night and "as long as needed", Assistant Commissioner for Specialist Crime and Operations Mark Rowley said
- With dozens of witnesses to the killing, police are urging them to contact the Met's anti-terrorism hotline with information
- The scene continued to be searched as police gather forensic evidence, both in relation to the murder and in relation to the actions of police
- In Saxilby where several streets have been cordoned by police, the chairman of the parish council said: "We are absolutely shocked that our friendly village has been caught up in this terrible incident."
Mayor of London Boris Johnson said it would be wrong to blame the killing on either Islam or British foreign policy.
Visiting the scene, Mr Johnson said: "Plainly this was a horrific incident. Everything that I have seen and heard this morning leads me to conclude two things: that those guilty will be brought speedily to justice and second, I have no doubt that Londoners can go about their lives in the normal way today."
Mr Cameron highlighted the actions of cub scout leader Ingrid Loyau-Kennett as demonstrating "confronting extremism is a job for us all".
"When told by the attacker he wanted to start a war in London, she replied, 'You're going to lose. It is only you versus many.' She spoke for us all," Mr Cameron said.
According to the Daily Telegraph Ms Loyau-Kennett asked the man: "Would you like to give me what you have in your hands?"
"He was covered with blood," she said. "I thought I had better talk to him before he starts attacking somebody else."
She says the suspect told her the dead man was a British soldier, adding: "I killed him because he kills Muslims over there and I am fed up that people kill Muslims in Iraq and Afghanistan."
The Muslim Council of Britain said the murder was "a truly barbaric act that has no basis in Islam and we condemn this unreservedly".
Communities Minister Baroness Warsi said there would always "be individuals and groups who will try and use these moments to divide us... but I think what we are seeing coming out of this tragedy and what is emerging is faith communities coming out together and showing a unified condemnation of this."
Meanwhile, armed forces personnel based in London and elsewhere have been told to be more vigilant.
That is on top of the extra precautions now being taken at London's 10 or so main barracks.
Chief of Defence Staff General Sir David Richards: "This was outside the base and I am confident that security is as tight as it has ever been. It is a very difficult balancing act. We are very proud of the uniform we wear. We have huge support around the country. I think this is a completely isolated incident - we will wait for confirmation - but that is my view."
He said there was "no reason we should not wear our uniforms with pride but on a common-sense basis".
BBC defence correspondent Caroline Wyatt said that, since British forces intervened in Iraq and Afghanistan, they and their families have been well aware they might be targets at home.
At least two plots by Islamist extremists to kill soldiers in the UK have been foiled in recent years.