The actor, who in his latest film, Imperium, plays an FBI agent who infiltrates a right-wing extremist bomb plot, says "the vast majority of voters aren't racist extremists".
Yet, he continues: "Something's happened with Brexit and with Trump, people can now hear these views on TV and believe it's a legitimate way to think about people."
He says he feels it's now harder to be patriotic in the wake of the UKs vote to leave the EU.
"Some people will think you're racist. Patriotism is linked to nationalism and it's not the same thing," he says.
"I view myself as very patriotic but it's got nothing to do with the idea of wanting to be separate from Europe. We're an island, but a mix of cultures and languages has made us what we are. It's very sad to watch people think it's not the case."
Imperium was made last year, the actor explains, "when I couldn't have anticipated any of these views expressed in the film being mainstream. Trump was a joke candidate".
The film, co-starring Australian actress Toni Collette, is a collaboration between its writer-director, American Daniel Ragussis, and former FBI agent Mike German, who provides the inspiration for Radcliffe's role as Nate Foster. German was an undercover infiltrator in Far Right movements for years, leading to many arrests.
However, despite some high-profile attacks, most notoriously the Oklahoma bombings in 1995, carried out by white supremacist Timothy McVeigh, Ragussis believes the focus on so-called Isis-inspired terrorism means coverage of Far Right violence is no longer prominent.
"White supremacist groups are not necessarily classified as terrorists," he explains.
"I feel like we don't have to draw attention to people inspired by Isis," adds Radcliffe. "When the bomb went off in New York, I was saying to myself 'please don't let the perpetrator be black, or Muslim - because then it will be used by Trump'. But we do need to draw attention to the Far Right's activities."
The actor says his Jewish heritage "wasn't a deciding factor in making this film".
"It's also to do with my Dad coming from Northern Ireland. The film makes the point that terrorism comes in a lot of forms.
"I know from my Dad being Irish, that white people do this too. I think it's useful to remind people of that right now."
Radcliffe adds that he "dipped into" Adolf Hitler's 1925 autobiography, Mein Kampf, and expresses the hope that neo-Nazis would watch Imperium.
"I don't care if they do it as some kind of hate activity because I am Jewish, I feel that this is the kind of film they might watch because, while we don't have an open mind about their ideas, we do have an open mind about white supremacists as people - if you watch the film, not everyone in there is a skinhead, they are not portrayed as monsters."
However, it was Radcliffe's shaved head, done during a scene in the film, that gave Imperium most publicity as the first pictures caused an internet sensation when they were first released last year.
"It shouldn't be news that someone got a haircut but I guess that's ultimately good for the film," says Radcliffe.
He says he also accepts, although doesn't understand, why five years since the last Harry Potter film, such fan frenzies occur.
"I have sat next to actors in interviews and listen to them give answers to media questions and think, 'I could never say that, that will go everywhere'. It's super weird - I've got better at dealing with it though.
"I'll just keep on making different choices to do different films - and the fact that they are all so different these days isn't a comment on my role as Potter, I just don't want to repeat myself.
"So no one should ever expect a re-run of Woman in Black, Kill Your Darlings, or Imperium at all."
Imperium is released in the UK on 23 September 2016
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Daniel Radcliffe believes that the UK's Brexit vote, along with the rise of Donald Trump, has made the Far Right "now a legitimate part of political discussion".