The BNP leader Nick Griffin was repeatedly pilloried and criticised on the BBC's Question Time tonight when he was dubbed the "Dr Strangelove" of British politics after attempting to claim the mantle of Winston Churchill and struggling to explain his denial of the Holocaust.

In passionate exchanges on the BBC's flagship current affairs programme, a black member of the audience accused Griffin of "completely disgusting" behaviour as he was forced to explain why he had met a Ku Klux Klan leader and attacked Islam.

Griffin was booed when he walked into the studio for the show's recording a few hours before it was broadcast at 10.35pm.

A police helicopter hovered over the BBC Television Centre in west London while the recording took place, after 25 anti-fascist demonstrators had earlier broken through police lines to get into the foyer. Up to 1,000 demonstrators protested outside as television centre was "locked down" during an operation in which three police officers were injured.

In the first question, the panel was asked whether it was fair that the BNP had hijacked Winston Churchill. Griffin said that the wartime prime minister would have been a member of the BNP. "I said that Churchill would belong in the BNP, because no other party would have him for what he said in the early days of mass immigration into this country, the fact that they are 'only coming for our benefits system', and for the fact that in his younger days he was extremely critical of the dangers of fundamentalist Islam in a way which would now be described as Islamophobic."

In one of a series of hostile interventions from the audience, a young black Briton called Griffin disgusting, and accused him of poisoning British politics. "For just one minute, could you not think of the benefits that my parents brought to this country? No. All you're thinking of doing is poison politics. The vast majority of this audience find what you stand for to be completely disgusting." As the audience cheered, Griffin said he had been portrayed as a monster because of "outrageous lies".

Asked by the Question Time presenter David Dimbleby what had been untrue, Griffin said: "The vast majority of them, far too many to go into." As the audience laughed at Griffin's refusal to detail what he called lies, Dimbleby asked whether he had denied the Holocaust. "I do not have a conviction for Holocaust denial," he replied.

As Dimbleby asked why he had denied the Holocaust, Griffin smiled. "Why are you smiling, it is not a particularly amusing issue," the presenter asked.

Dimbleby threw some of Griffin's quotes back at him. "Ethnicity – 'I want to see Britain become 99% genetically white, just as she was eleven years before I was born'. Right? You say you are misquoted. I can't find the misquotations."

Griffin did not challenge the Dimbleby quotes but denied a quote in the Daily Mail that he had said that black people walked like monkeys. He then struggled as a young Jewish man wearing a skullcap challenged him to explain why he had likened the "orthodox opinion" that six million Jews were killed in the Holocaust to the old "orthodox opinion" that the earth was flat.

The audience member said: "Sir Winston Churchill put everything on the line so that my ancestors wouldn't get slaughtered in the concentration camps. But here sits a man who says that is a myth just like a flat world was a myth."

Griffin was jeered as he struggled to explain his stance on the Holocaust. "I cannot explain why I used to say those things," he said as he blamed his inability to spell out his thinking on the threat of being deported under the European arrest warrant to France and Germany where Holocaust denial is illegal.

Jack Straw, the justice secretary, said there was no law preventing Griffin from explaining himself. Griffin said he now accepted that Jews were murdered after hearing British radio intercepts of German transmissions which showed there had been a mass murder of Jews on the eastern front. "What about Auschwitz," Straw asked of the extermination camp in Nazi-occupied Poland. "You don't need a subsequent radio intercept to find out that people were gassed at Auschwitz."

The justice secretary dubbed Griffinthe Dr Strangelove of British politics — referring to the German scientist, played by Peter Sellers, who keeps referring to the US president as Mein Fuhrer.

A British Asian man was clapped when he accused Griffin of wanting to hound him out of Britain. "You'd be surprised how many people would have a whip-round to buy you a ticket and your supporters to go to the South Pole. It is a colourless landscape that will suit you fine."

In a sign of the BBC's determination to put pressure on Griffin, Dimbleby asked why he had met Ku Klux Klan leader David Duke. Griffin said Duke was a non-violent figure, prompting laughter.

The panel was also asked why Islam is a "wicked and vicious faith" – a reference to remarks by Griffin. He said there were good points to Islam because it opposes usury, but added: "It [Islam] doesn't fit in with the fundamental values of British society – free speech, democracy and equal rights for women."

Griffin insisted he was not a Nazi. "I have been relentlessly attacked and demonised in the last few days ... I am not a Nazi and never have been."

Lady Warsi, shadow cohesion minister, said: "Mr Griffin is obviously a confused man. On the one hand he says he does not believe in lots of values he attributes wrongly to Islam. Yet it was Mr Griffin who shared a platform with Abu Hamza."

The BBC, which has faced intense criticism, believed the tough questioning vindicated its decision. "Members of the audience asked the kind of tough questions that mark Question Time out as the premier television programme," the BBC deputy director general, Mark Byford, said. Straw said: "We see here a fantasising conspiracy theorist [who] madly defines his politics by race rather than by moral values."