Arron Banks has insisted there is "no evidence" his pro-Brexit campaign Leave.EU took any Russian money.
Earlier, Mr Banks told the committee he does not have any business interests in Russian Federation.
"I met with him, I'm a businessman, why shouldn't I?"
"I pay a shed-load of tax, probably more than the entire committee put together", he said. After the warnings, Banks said, the deal fell away.
The committee is quizzing Banks about his possible ties to Russian Federation, after the Sunday Times said his ties to the country went further and deeper than he had previously disclosed. But as the hearing was towards the close Mr Banks - a close friend of Nigel Farage - suddenly cut it short as he had "places to be".
MPs repeatedly questioned Banks, an insurance entrepreneur, about the sources of his money, prompting Banks to deny any of his wealth that he used to pump at least £9m of loans and donations to the Brexit campaign was from Russian Federation.
But Mr Banks snubbed his pleas and walked off as his aide Andy Wigmore - who was also being interrogated by MPs - revealed they were heading for the House of Commons bar.
Previous to Banks and Wigmore's French exit the pair had been under fire for alleged links to Russian Federation.
The suggestion that Banks meet Povarenkin followed a meeting with Russia's ambassador to Britain, Alexander Yakovenko, in November 2015.
Wigmore told the committee on Tuesday that he had requested the meeting with the Russian officials.
He said: 'Sorry, I really have to insist.
"You've got to see the genesis of where this all came from".
When Mr Collins again pressed for five more minutes, Mr Banks responded sternly: "No, no, no - the word is "no". Echoing his phrase, Banks agreed: "Many good lunches".
The head of the parliamentary inquiry into "fake news", Conservative MP Damian Collins, said the report raised serious questions about Russian interference in United Kingdom politics.
In a tense exchange, Mr Banks tells the committee it has already run late and he has to leave to go for lunch. "What's wrong with that? We gave them a telephone number", Banks said.
He acknowledged giving the Russian ambassador the telephone number of Donald Trump's transition team before the president won the USA election.
Leave.EU was fined £70,000 by the Electoral Commission earlier this year for breaches of election law in the Brexit referendum. Collins told the committee that as a result it would not be possible for the committee to explore related areas.
Appearing before the MPs' committee investigating so-called "fake news", Mr Banks confirmed Leave.EU held talks with controversial data firm Cambridge Analytica and meant to use its services if it had been selected as the official Leave campaign - which it was not.
"I didn't know that Roman Abramovich was Putin's number one man in London, but you may know more than I do". The MP said: "Chelsea won 2-1, that was the extent of the entertainment".
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