Neil prised apart Hopkins' argument that the US billionaire had shown "true leadership" in proposing a ban on Muslims entering the United States, by getting the Mail Online columnist to admit she didn't actually support Trump's controversial plan.
The veteran interviewer also took on Hopkins' claims of BBC bias and revealed that her views around Britain's Muslim population appeared not to be based on any facts.
Hopkins began the interview with a broad overview of her views on Trump, following her Mail Online column in which she lended him her support.
"What I was saying is that I support the ideas behind what he’s trying to do," she said.
"Ultimately, Donald Trump is trying to show true leadership. The Americans felt very let down by what Obama had to say the day after 14 people were gunned down.
"In that kind of vacuum what you see is that Donald Trump stands up and he says something that sounded like he wanted to protect his nation, protect America, and that's what I stand behind."
Yet in a revealing exchange, Hopkins revealed she didn't actually support the Republican hopeful's proposals.
“You can’t enforce that sort of thing, you can’t have religion announced on your passport," she said.
"What are we going to do? Eat a hot dog and sing 'Glory Glory Hallelujah'?"
Challenged by Neil on her apparent hypocrisy, Hopkins attempted to re-frame her support as being for Trump's "true leadership".
"You can knock the specifics but that's the true leadership," she said.
However, desperate to interject, Hopkins said: “Let’s talk about the people who do support what Trump says.”
But the presenter immediately shut her down, sternly telling here: “Hold on, I ask the questions.”
But it was an early accusation of BBC bias which set the tone for the exchange, provoking Neil to employ rapid rebuttal.
"I'm actually, personally a little tired of your BBC bias which of course keeps telling us that most people support banning Trump from the UK but actually it's only 500,000 clicking on a mouse," she said.
Neil quickly interjected to ask: "When did I say most people are in favour of banning him?"
"Well you went through a long list didn't you, Boris Johnson, people clicking on a petition," Hopkins responded.
Neil responded: "I have no evidence of the views of most British people."
Neil then moved to Hopkins' suggestion that there are "vast swathes of the UK" that are not safe.
“There are plenty of places in the UK that I would not walk through," Hopkins said.
“I don’t think it’s legally accurate to name specific areas..”
Neil responded: “There’s no legal issues, tell us these vast swathes.”
Yet despite Neil's efforts, Hopkins refused to name places she believed to be unsafe, despite claiming areas where nine out of 10 people are Muslim presented unacceptable risks.
But Hopkins' claims around areas with a Muslim population of over 90% are not borne out by the facts.
The 2011 census found the highest proportion of Muslims residing in a local authority area to be well below nine out of ten residents.
Some 34.5% of those living in the London Borough of Tower Hamlets identified as followers of Islam, making it the area with the highest percentage Muslim population, according to the ONS.
Viewers were quick to compliment Neil's handling of Hopkins.
Very satisfying to watch Andrew Neil take Katie Hopkins apart on her deluded Islamophobia nonsense #BBCDP— Liberals for Indy (@Liberals4Indy) December 11, 2015
@afneil is making Katie Hoplins look like a fool on the Daily Politics. Not hard, but entertaining nonetheless!— Rhodri Day (@Rhod_Dayo) December 11, 2015
Thank goodness for Andrew Neil. https://t.co/NR37HRMZKv— Andy Russell (@Andy_Russell_) December 11, 2015
'Katie Hopkins that isn't how polls work' - Andrew Neil— Adina (@DinaRayy) December 11, 2015
Hopkins' appearance on the BBC's 'Daily Politics' came after she wrote of her admiration for Trump announcing his plan, despite apparently not agreeing with it herself.
On Thursday, Donald Trump thanked "respected columnist" Katie Hopkins for her support, saying she has provided "powerful writing on the UK's "Muslim problems".