"You are truly welcome, welcome to London, a city of all faiths," Livingstone said.
But not all Britons have been as welcoming. The controversial cleric's tour has raised protests from politicians, Jews, gays, and even some British Muslims.
Al-Qaradawi, who is 77, has condoned suicide bombings as an acceptable tactic for Palestinians -- a view that has banned him from traveling to the United States. But he is a frequent visitor to Britain.
His arrival sparked a sharp exchange in the British Parliament between Prime Minister Tony Blair and opposition leader Michael Howard.
"When I was home secretary [interior minister], I used my powers to ban people whose presence here was not conducive to the public good. I banned them. Why doesn't [Blair's] home secretary do the same?" Howard said.
Blair's reply was similarly heated.
"This is not a party political issue, for goodness' sake. We are totally opposed, as is everyone, to people coming to this country and using it as a platform for views in support of terrorism or extremism of any sort at all," Blair said.
But Britons are clearly divided over whether al-Qaradawi's views support terrorism.
The cleric has criticized the 9/11 terrorist attacks on America, and has criticized Muslim extremists.
But he has also called for the "destruction" of Jews, called homosexuality a perversion that should be punishable by death, and says men should beat wives who are disobedient.
Jerry Lewis is a member of the Board of Deputies of British Jews, which had called for the cleric to be banned from visiting.
"It is inflammatory, it is damaging for race relations in this country. And we have gone to the police and said please exclude this cleric, he is not what he seems to be. People are calling him a moderate -- he is no moderate. He's got very extreme views, and we have to make sure that people like him are not allowed entry in this country," Lewis says.
Al-Qaradawi is considered one of the spiritual leaders of the Muslim Brotherhood, an organization that has been banned in Egypt and several other Middle East countries. He has been based in Qatar since 1961, and hosts a weekly talk program on the Al-Jazeera television station.
Many Muslims see the cleric as one of Islam's more balanced voices. Shabana Khan is spokeswoman for the Muslim Council of Britain, an affiliate of the Muslim Association of Britain, which is sponsoring al-Qaradawi's visit.
"Our basic position is that Dr. Qaradawi is actually one of the moderate voices in the international community, who is calling for greater understanding between the various faith communities, and I think it's very unfortunate that newspapers and the press in the UK have stirred up the situation," Khan said.
But other British Muslims are more skeptical. Ghayasuddin Siddiqui is a member of the Muslim Parliament of Great Britain. He says al-Qaradawi has made what he calls "very unfortunate and unacceptable remarks." But he does not say that is enough to justify banning the cleric from visiting the country.
"What upsets the Muslims in this country is that when [French nationalist politician Jean-Marie] Le Pen came -- he is an equally undesirable person -- there was no demand that his entry be banned," Siddiqui said.
Al-Qaradawi's speeches have been carefully monitored throughout his visit, which ends today with an appearance at a conference supporting the right of Muslim women to wear the hijab.