The two terror suspects being held under armed guard at hospitals in London were both known to security services, Government sources say.
The men - who were apparently assessed by MI5 as not posing a threat requiring "immediate intervention" - were arrested following the hacking to death of a serving soldier in the street in Woolwich, southeast London.
Sky's crime correspondent Martin Brunt said one suspect had been identified as Michael Adeboloja, a 28-year-old Londoner of Nigerian descent.
Police investigating the attack have been searching an address in Greenwich and another in Lincolnshire, believed to be connected to Adeboloja.
Brunt added: "We believe it is his father's house that is being searched by Lincolnshire Police on behalf of counter-terrorism command at Scotland Yard."
Relatives of the dead soldier are believed to have been informed and his identity is expected to be released later today. A post mortem is being carried out on the body.
A Facebook page in honour of the Woolwich victim has received around one million 'likes'.
Counter-terrorism officers are leading the investigation into the "shocking and horrific" murder and the Prime Minister has held talks with his top advisers to address potential security implications.
Two suspected Muslim fanatics attacked the man in the street a short distance from the Royal Artillery Barracks after apparently knocking him down with their car.
Witnesses said they set about the soldier with a number of weapons, which appeared to include knives and a meat cleaver, while shouting the name of "Allah".
They apparently encouraged passers-by to video them. One of the alleged attackers was filmed wielding a bloodied meat cleaver, saying: "We must fight them as they fight us. An eye for an eye, a tooth for a tooth.
"I apologise that women have had to witness this today, but in our land our women have to see the same. You people will never be safe. Remove your government, they don't care about you," he said.
Armed officers arrived about 20 minutes after the attack began and shot two suspects, with one in a serious condition. According to sources, one of the suspects is being treated in King's College Hospital, Camberwell.
Scotland Yard said on Thursday that officers were at the scene within nine minutes of receiving that first 999 call.
"Firearms officers were there and dealing with the incident 10 minutes after they were assigned, 14 minutes after the first call to the Met," Assistant Commissioner Simon Byrne said.
Scotland Yard's police commissioner, Sir Bernard Hogan-Howe, confirmed that the two men had been arrested.
"We understand concern about the motivation and we will work tirelessly to uncover why this occurred and who was responsible. I understand people want answers, but I must stress we are in the early stages of investigations," he said.
Anjem Choudary, the former leader of banned Islamic group al Muhajiroun, said he knew one of the alleged attackers but had not seen him for about two years.
One of them was also reportedly stopped as he attempted to leave the country for Somalia to join al Shaabab militants.
Jahan Mahmood, a community worker who has advised the Home Office and British Army on Muslim affairs, said an attack of this nature had "been coming for a long time".
"I don't know how we can deal with these people, who appear to be individuals acting alone."
About 1,200 extra police officers have been deployed across London and security has been stepped up at military barracks across the capital.
Forensic officers were still on the scene on Thursday morning and the area remained cordoned off. The car used in the attack was taken away during the night.
After it became clear through eyewitness accounts that the attackers had political and religious motives, the Government held a so-called Cobra emergency response meeting, which was followed by another this morning.
Prime Minister David Cameron said afterwards: "The people who did this were trying to divide us. They should know something like this will only bring us together and make us stronger.
"One of the best ways of defeating terrorism is to go about our normal lives."
The Muslim Council of Britain said it had received "reports of hate attacks and abuse faced by mosques and individual Muslims following the inexcusable and criminal murder".
The group called for solidarity between "all our communities, Muslim and non-Muslim".
Riot police had to contain an English Defence League demonstration in Woolwich after the murder, while elsewhere two mosques were attacked.
The barracks, also known as the Woolwich station, houses a number of the King's Troop Royal Horse Artillery and independent companies of the Grenadier and Coldstream Guards.
:: Police have issued an appeal for anyone who has still or moving images of the incident to send them to: email@example.com
They asked anyone sending in images to include their name and contact details, which they said would be treated in the strictest confidence. Alternatively, those with footage can contact the police's anti-terrorist hotline on 0800 789321.