Andy Wigmore, who ran the Ukip-led Leave-EU campaign, also admitted it “completely, completely, completely” copied Donald Trump’s tactic of making “outrageous” statements.
Meanwhile, the chief executive of the parent company of scandal-hit Cambridge Analytica was recorded saying Mr Trump deliberately portrayed Muslims as “an artificial enemy”, in the same way that Adolf Hitler played on German hatred for Jews.
Cambridge Analytica made presentations for Leave-EU for the Brexit campaign, but did not work formally the organisation, Nigel Oakes said.
Nevertheless, the head of a Commons committee which is investigating the Cambridge Analytica data scandal, said people would be “very frightened” by the interviews.
Damian Collins said the Nazi tactic was “to create bogeymen for people to be frightened of” and that its inquiry wanted to determine “were these tactics being used in the referendum campaign”.
“Does modern techniques allow data profiles to be built up of people that makes it much easier to target people in this way,” asked the chairman of the digital, culture, media and sport committee, speaking on BBC Radio 4’s Today programme.
Mr Collins suggested that, despite Cambridge Analytica not signing a contract with Leave-EU, “a huge amount of work was done which I believe they benefited from”.
“People will be very frightened to think that people like Nigel Oakes and Andy Wigmore would have access to their data and could therefore target them in this way,” he said.
Brexit talks: Top issues facing UK on leaving EU
Both figures were among a number of political campaigners who spoke to Essex University researcher Emma Briant for an upcoming book on the Trump campaign.
Mr Wigmore told her: “The propaganda machine of the Nazis, for instance – you take away all the hideous horror and that kind of stuff, it was very clever, the way they managed to do what they did.
“In its pure marketing sense, you can see the logic of what they were saying, why they were saying it, and how they presented things, and the imagery.
“And looking at that now, in hindsight, having been on the sharp end of this campaign, you think: crikey, this is not new, and it’s just … using the tools that you have at the time.”
He added that Leave.EU “completely, completely, completely” copied Mr Trump’s technique of making attention-grabbing and controversial comments.
“The only way we were going to make a noise was to follow the Trump doctrine, which was, the more outrageous we are, the more attention we’ll get, and the more attention we get, the more outrageous we’ll be. And that’s exactly what we did.”
Mr Wigmore defended the recording on the basis that the Nazis came up for discussion “in a historical context”, in reference to the tactics being used by the Remain campaign.
He added: “Immigration was the key issue in pretty much all polling.
“Facts are not scare tactics, if that’s what people feel is their concerns, and it was our opinion that we had to keep that top of the agenda in line with our polling and the strategy of Nigel Farage.”
Cambridge Analytica said Mr Oakes had never worked for the company and “did not work on the Trump campaign in any way whatsoever”.