Government security services will face an inquiry from the House of Commons after it was confirmed the two men arrested, Michael Adebolajo, and Michael Adebowale, were known to the British domestic security agency MI5, the BBC reported.
Prime Minister David Cameron said there would be a full investigation by Parliament's Intelligence and Security Committee amid outrage both suspects were known to MI5 but neither was considered a major security risk.
Drummer Lee Rigby, 25, of the 2nd Battalion, the Royal Regiment of Fusiliers, was run over and attacked with butcher knives and meat cleavers Wednesday as he walked back to his barracks in south London's Woolwich district.
His alleged killers remained under armed guard in separate London hospitals.
A man believed to be Adebolajo was videotaped by a passerby, saying he carried out the attack because British soldiers killed Muslims every day, the BBC said.
Speaking on a BBC morning television program, Communities Secretary Eric Pickles said Parliament "will do a thorough investigation in terms of what the security forces knew, but I've seen experts on security explaining how difficult it is in a free society to be able to control everyone."
Richard Barrett, former head of counterterrorism at MI6, the British military intelligence agency that concentrates on foreign threats, said it was difficult to detect potentials attacks of the type that killed Rigby.
"When does a person who expresses radical views, who joins a radical group, flip over to be a violent extremist? To find the signals, the red flags as it were, I think is enormously hard."