The chief executive of the big data marketing firm Cambridge Analytica has denied claims by a prominent Brexiter that his company worked on a pro-leave campaign during a tense hearing in front of a House of Commons committee.

Alexander Nix told the digital, culture, media and sport committee inquiry into fake news that Cambridge Analytica had never worked on the Brexit referendum, despite claims that it had partnered with Leave.EU, the unofficial pro-Brexit campaign co-founded by Arron Banks.

“We did not work with them,” Nix told Damian Collins, the Conservative chair of the committee. “So however you look at this, or however it appears to you, or whatever tweets other people have said about this situation, we did no paid or unpaid work, we had no formalised relationship with [Leave.EU], we did not work on the EU referendum with that organisation or any other organisation.”

But while Nix was still in front of the committee, his claims were challenged by Banks himself, who tweeted: “Cambridge Analytica appeared in the submission document” that Leave.EU had filed when it was trying to become the official leave campaign, a position later filled by the Boris Johnson-backed Vote Leave. That public document notes Cambridge Analytica as a “strategic partner”.

Banks also tweeted: “CA wanted a fee of £1m to start work & then said they would raise £6m in the states. We declined the offer because it was illegal.” When Banks’s tweet was read out during the hearing, Nix described it as “absolutely incorrect”. “Look, Mr Banks is at liberty to say whatever he likes, but I don’t have to agree with it,” he added. “That is totally untrue.”

In response, Banks tweeted: “Nix & Cambridge Analytica are compulsive liars.”

The indirect spat between the two men came in the midst of a hearing in which the culture committee grilled Nix on Cambridge Analytica’s business practices. The company has been the subject of persistent accusations that it intervened in the EU referendum, and that it infringes people’s privacy through its use of targeted advertising, which involve using massive amounts of purchased personal data to better target people with political and commercial messages.

Nix argued that the claim that Cambridge Analytica was involved in the referendum was itself fake news stemming primarily from the “erroneous” publication of an article in Campaign magazine, attributed to Nix, which said that “Cambridge Analytica has teamed up with Leave.EU … to help them better understand and communicate with UK voters”.

“The moment that that statement went out,” Nix said, “we were absolutely crystal clear to all the media outlets that we weren’t involved, that it had been released in error, and we tried to correct the press again and again and again.”

Nix also addressed a claim from Julian Assange that Cambridge Analytica had attempted to work with WikiLeaks during the US election. After initially telling the committee that the two groups had “no relationship – period”, Nix later stated that Cambridge Analytica had reached out to Assange through his agent in an effort to secure material about Hillary Clinton that the firm believed WikiLeaks held. “We received a message back saying, ‘No, they wouldn’t meet,’” Nix said. “That was it. We, like everyone else, were keen to find out what this data was.”