The BNP leader Nick Griffin was booed at the start of the recording of Question Time and was accused of trying to "poison politics" as he was attacked by fellow panellists and the audience.
The show 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.
He was asked by a member of the audience about why he had described Islam as a "wicked and vicious faith".
The BNP leader insisted his views had been widely misrepresented in the media and denied a string of statements attributed to him, including a quote from 2006 in which he said "Adolf went a bit too far".
"I am not a Nazi and never have been," he said, adding: "I am the most loathed man in Britain in the eyes of Britain's Nazis."
But Mr Griffin was 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."
The BBC defended its decision to ask Mr Griffin onto the show.
"The BBC is firm in its belief that it was appropriate for Mr Griffin to appear as a member of the panel and the BBC fulfilled its duty to uphold due impartiality by inviting him on the programme," said its deputy director general Mark Byford.
Six protesters were arrested and three police officers injured during demonstrations outside BBC Television Centre, where the programme was filmed.