Banks' snub comes after the communications chief of Vote Leave, which won official designation as the lead Brexit campaign group ahead of Leave.EU, also refused to appear, prompting Britain's parliament to take the rare step of ordering him to come.
Banks and Wigmore were introduced to Yakovenko by Alexander Udod, a suspected Russian spy who was expelled from the United Kingdom after the poisoning of Sergei and Yulia Skripal.
"This is really important for us to understand why someone like Mr Banks had this level of contact with the Russian government, maybe more of it, a contact that he'd not denied having but certainly downplayed the number of times he'd met with them and the significance of those meetings", he said.
But Banks told the paper: "I had two boozy lunches with the Russian ambassador and another cup of tea with him, bite me".
Banks visited Moscow in February 2016, was offered a business deal involving six Russian goldmines, and even invited Yakovenko to a party on the day of the referendum, the emails show.
The scale of the pair's links to Russian Federation is revealed in a series of 40,000 emails obtained by the former Sunday Times journalist Isabel Oakeshott, who ghost-wrote Mr Banks's Bad Boys of Brexit book.
Millionaire Brexiteer Arron Banks has denied visiting Russian Federation during the European Union referendum amid calls for police to investigate his Kremlin links.
Some Trump aides are under investigation in the U.S. over whether they colluded with Moscow and there are also claims that Moscow tried to meddle in Britain's referendum campaign to encourage a Brexit vote.
"Did that happen? Did he make money out of it and did he use that money to fund his campaigns?"
Asked about the report at the G7 summit in Quebec on Saturday, Theresa May said: "I am sure that if there are any allegations that need investigation the proper authorities will do that".
Yes, Trump Talked About Human Rights With Kim Jong Un - Katie Pavlich
Told by doctors he would never recover, the parents agreed to remove him from life support and he died six days later , age 22. Warmbier was evacuated in a coma on June 13, 2017, and returned home to his family in Cincinnati.
"It's a convenient witch-hunt, both over Brexit and Trump", he added, referring to allegations of Russian meddling in the 2016 USA presidential election.
She came forward after her email accounts were hacked, according to the newspaper.
Banks and his ally, Wigmore, made repeated contact with Russian officials before the referendum to discuss business opportunities.
Lawmaker Damian Collins said his committee plans to question Arron Banks, co-founder of the Leave.EU campaign group, later this week.
"We didn't profit from any business deals because I never pursued anything", he said.
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 United States president-elect in November 2016 in NY.
He told the paper he had also disclosed details of his contacts with the Russians to USA officials.
Labour leader Jeremy Corbyn claimed Mr Banks "probably has questions to answer", while Cabinet Office minister David Lidington said: "Clearly they are serious allegations but we have, in this country, a system where there are independent agencies to look at allegations of malpractice".
The Russian embassy has said it has not intervened in United Kingdom domestic politics.