They were also said to have met Alexander Udod, one of 23 suspected Russian intelligence officers ejected from the United Kingdom after the poisoning of Sergei and Yulia Skripal in Salisbury.
The paper said that Mr Banks and Leave.EU director of comunications Andy Wigmore had also had lunch with the ambassador in November 2016 - just three days after they and the former UKIP leader Nigel Farage had met Donald Trump in NY following his election victory.
But Banks dismissed the claims, telling the paper: "I had two boozy lunches with the Russian ambassador and another cup of tea with him".
Mr Banks had previously spoken of a six-hour lunch with ambassador Alexander Yakovenko but reports at the weekend, based on leaked emails, pointed to further meetings that included discussions on a business opportunity involving Russian gold mines.
Mr Collins agreed there is no suggestion Mr Banks had done anything wrong, as he is a private businessman, but added: "Russia is not a friendly country, Russian Federation has a track record of interfering in the politics of other countries, directly and indirectly".
Ultimately, Leave.EU lost the battle to be designated the official "leave" campaign to rival organisation Vote Leave.
When asked about the claims during a press conference at the G7 summit in Quebec, Prime Minister Theresa May said: "I am sure that if there are any allegations that need investigation the proper authorities will do that".
The Sunday Times said emails it had seen from Mr Banks and Leave.EU communications chief Andy Wigmore showed they had repeated contacts with Russian officials to discuss matters of mutual interest throughout the EU referendum campaign and its aftermath.
Ms Oakeshott passed them to the paper after her email accounts were "hacked".
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Banks has also reportedly admitted that he handed over phone numbers for members of Donald Trump's transition team to Russian officials, after meeting with the USA president-elect in November 2016 in NY.
"It's a convenient witch-hunt, both over Brexit and Trump", he added, referring to allegations of Russian meddling in the 2016 US presidential election.
LONDON, June 8 (Reuters) - Arron Banks, the founder of Brexit campaign group Leave.EU, pulled out of a hearing with a parliamentary committee, saying on Friday it had been conducting a witch hunt of those who want Britain to leave the European Union.
Writing in the paper, Oakeshott said: "Banks and Wigmore were shamelessly used by the Russians".
He told the paper he had also disclosed details of his contacts with the Russians to U.S. officials.
Meanwhile, Mr Wigmore denied handing over any Brexit-related information.
Banks and Wigmore were invited back to meet Yakovenko after they, and Brexit firebrand Nigel Farage, met with Trump in November 2016 shortly after his election.
David Lidington, May's de facto deputy, also called for an investigation.
The Russian Embassy insists that it "has not in any way intervened in the domestic United Kingdom political process, including the Brexit referendum" and that meeting stakeholders from across a country's political spectrum is a "natural element of the work of any embassy".