The BBC has defended the invitation to the leader of the anti-immigration party to appear on the programme, saying it had a duty to be impartial.
During the show the panel covered topics including whether it was fair for the BNP to "hijack" images of Winston Churchill, whether immigration policy had fuelled the BNP's popularity and whether Mr Griffin's appearance was an early Christmas present for the party.
Justice Secretary Jack Straw said what distinguished the BNP from other parties was that other parties "have a moral compass", adding: "Nazism didn't and neither I'm afraid does the BNP."
If there is a case for censorship, it should be debated and decided in Parliament. Political censorship cannot be outsourced to the BBC or anyone else
If Nick Griffin's appearance on Question Time has the ultimate effect of shaking the 'great' british public free of their political apathy and encourages them to ask probing questions, then his appearance will be a good thing
Asked whether immigration policy had fuelled the BNP, Mr Straw said he did not think it had and said he thought the BNP had been boosted by discontent with the main parties over issues like expenses.
But Baroness Warsi said politicians had a responsibility to take on the BNP on the issue of immigration: "Many people who vote for the BNP are not racist and therefore what we have to do is go out and say to these people as mainstream political parties we are prepared to listen."
Mr Griffin blamed the "political elite" for imposing "an enormous multicultural experiment on the British people".
But his references to Britain's "indigenous people" prompted other members of the panel to challenge him to say he meant white people.
Mr Griffin said the colour was "irrelevant" and said Mr Straw would not dare go to New Zealand and tell a Maori he was not "indigenous". "We are the aborigines here," he claimed.
Protesters storm into BBC Televison Centre
But he was accused of making up facts. He was also challenged by several black and Asian members of the audience.
One man asked Mr Griffin: "Where do you want me to go? I love this country, I'm part of this country."
Following the programme, Mr Griffin told BBC News too much of the programme had been a a beat up Nick Griffin programme instead of Question Time".
He added that of the 25 or so allegations made against him in the programme - he was only allowed to answer four or five of them and that was "grossly unfair".
While the programme was being recorded the anti-BNP protest continued, with the whole west London BBC building "locked down" for more than an hour and the road outside closed.
The Metropolitan Police say six protesters were arrested and three police officers injured in the protests.
Mr Griffin accused the protesters of "attacking the rights of millions of people to listen to what I've got to say and listen to me being called to account by other politicians".
But Weyman Bennett from Unite Against Fascism accused the BBC of "rolling out the red carpet" to Mr Griffin and said his appearance on the flagship discussion programme "will lead to the growth of a fascist party" and promote violence against ethnic minorities.
It's not for the BBC to censor and say they can't be on
About 25 people managed to get through the gates and run towards the BBC building when security guards opened them to let in a car. A few minutes later they were led, dragged or carried back outside.
There were also protests outside BBC buildings in Bristol, Liverpool, Nottingham, Glasgow and Belfast.
Earlier on Thursday, BBC director general Mark Thompson said it was up to the government to ban the BNP from the airwaves if it felt Mr Griffin should not be allowed to take part in Question Time.
Welsh Secretary Peter Hain, who had tried to stop the broadcast, said: "The BBC should be ashamed of single-handedly doing a racist, fascist party the biggest favour in its grubby history."
But Prime Minister Gordon Brown said it was a matter for the corporation and he did not want to interfere with it, while Culture Secretary Ben Bradshaw said that most of the cabinet did not share Mr Hain's view.
BBC Deputy Director General Mark Byford said it had been "appropriate" to invite Mr Griffin to appear given the support the BNP received in the last European elections when it gained its first Euro MPs.
He said: "He was scrutinised and challenged along with the other panellists heavily by the audience, that was right in our view.
"It would have been quite wrong for the BBC to have said 'yes, you are allowed to stand in elections, yes you have a level of support that now meets the threshold but the BBC doesn't think that you should be on'.
"We have no views on the politics or the political leaders what we do hold absolutely dear is that due impartiality is a value we uphold and that's why Mr Griffin was on tonight."
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