Hani al-Sibai, an Egyptian, receives thousands of pounds in UK welfare benefits and lives in a large west London house owned by a housing association.
He is alleged to have played a part in the radicalisation of young men in the area, including Mohammed Emwazi, the Islamic State (ISIS) killer known as "Jihadi John".
The 54-year-old has been resident in Britain since the mid-1990s when he fled Egypt, where he was wanted as a suspected member of Egyptian Islamic Jihad, the group set up by Ayman al-Zawahiri, the Al Qaeda leader.
He is monitored by British security services and is understood to have faced a clampdown on his media and internet activities, according to 'The Times'.
More From This Section
Since September 2005, Sibai has been listed on the UN Security Council list of individuals linked to Al Qaeda and described as "a known figure within extremist circles".
In an interview with 'Al Jazeera' after the bombings on July 7, 2005, in which 52 people were murdered, Sibai is reported to have said: "If Al Qaeda indeed carried out this act, it is a great victory for it. It rubbed the noses of the world's eight most powerful countries in the mud."
The Security Council listing reads: "He uses an internet site, and other media, to support terrorist acts or activities undertaken by Al Qaeda as well as to maintain contact with a number of supporters around the world."
The UK Home Office said it did not comment on individuals.