The debate at the Oxford Union featuring BNP leader Nick Griffin and historian David Irving highlights fundamental questions about the limits to free speech.
Could Hitler have been stopped if his free speech had been limited?
Some protestors called for the debate to be cancelled, both because it might offend people and because it could stir up racial hatred.
But there are others who think people should be allowed to say whatever they think - regardless of the offence it might cause, and even if there is a potential threat to public order.
For some anti-fascist campaigners like Donna Guthrie, the fact that David Irving's views are offensive to large numbers of people is enough to prevent him from speaking.
"Irving is a Holocaust denier, and giving him a platform is an insult to the millions who were murdered by the Nazis."
Ms Guthrie - National Campaigner for the group Unite Against Fascism - said there had also been a rise in racial attacks whenever Nick Griffin's BNP party gained seats on local councils.
She added: "Free speech is not uncontrolled. Speech does not happen in a vacuum. We know that when a fascist organisation speaks, there are real consequences."
In Britain there are laws protecting our right to free speech. But they are so hedged with qualifications that there is still plenty of room for arguments.
British citizens are covered by the European Convention on Human Rights which states: "Everyone has the right to freedom of expression."
But it adds that governments can restrict free speech for, among other reasons, in the interests of national security, preserving public safety and for the prevention of disorder or crime.
For libertarians like Brendan O'Neill, editor of the anti-censorship website Spiked, the convention does not go nearly far enough in protecting his right to say whatever he likes.
"I believe that there should be no limits at all on free speech," he said. "No-one has the right not to be offended: that is the essence of a free society."
He said that those who try to censor debate because it might stir up trouble were under-estimating the intelligence of the audience.
"The only time free speech should be restricted is if there is a clear and imminent danger of violence," he said
"Otherwise, even if what is being said might be defined as inflammatory then we still should not censor it," he said. "People are not attack dogs - they are not automatically going to become violent if they hear controversial things."
"Rather, these views should be expressed and challenged. Otherwise these horrible ideas will not be defeated, but will survive and fester underground."
Jonathan Heawood, English director of the worldwide association of writers Pen, opposed a ban on the debate - but admitted it was a difficult issue, given the views of the two speakers.
"We don't take the position of 'anything goes' when it comes to free speech. There are sometimes legitimate arguments about legal issues and national security."
"However, although Irving's views about the Holocaust are an extremely distorted version of history, it is hard to maintain that they directly incite racial hatred."
Gay rights activist Peter Tatchell counters this with the example of Hitler and the rise of the Nazi party in Germany before the Second World War.
Are Nick Griffin and David Irving dangerous enough to ban?
In a piece entitled: "Do fascists have a right to free speech?" he writes: "It is possible that if there had been no free speech for Hitler and the Nazi Party in Germany during the early 1920s... they may not have grown in strength and influence.
"Denying them an opportunity to propagandise, gain respectability and enter the political mainstream might have thwarted their rise to power. Tens of millions of lives may have been saved if the free speech of Nazis had been suppressed early on."
He added: "In extreme circumstances, there should be intolerance of intolerance. Otherwise some people can use free speech and their human rights to undermine the human rights of others."
Monday's debate in Oxford is an uncanny mirror of a similar event in New York last September.
Then, as now, a controversial speaker who questioned the validity of the Holocaust - in this case Iranian president Mahmoud Ahmadinejad - was invited to address a prestigious academic institution - Columbia university.
Mr Ahmadinejad encountered a determined protest by Jewish and other demonstrators who argued that his views did not deserve a platform.
The speech went ahead however. Columbia's president - the jurist and free-speech expert Lee Bollinger - justified his decision to invite Mr Ahmadinejad.
He wrote at the time: "It is a critical premise of freedom of speech that we do not honour the dishonourable when we open the public forum to their voices."
"To commit oneself to a life - and a civil society - prepared to examine critically all ideas arises from a deep faith in the myriad benefits of a long-term process of meeting bad beliefs with better beliefs and hateful words with wiser words."