The millionaire Brexiteer refused to answer journalist Fatima Manji's questions.
"What other people accused of serious crimes get the opportunity to present their denials and influence the investigation on the BBC?" wrote Lord Adonis on Twitter.
Banks said: "There was no Russian money and no interference of any type".
He told the Andrew Marr Show that all the cash came from a UK-registered company, and repeated claims that he was being targeted by Remain-supporting politicians.
She, and many others, said the BBC should not be giving Banks a "platform" by interviewing him.
The Electoral Commission referred him to the National Crime Agency (NCA) on Thursday, saying that it had grounds to believe that he was not the source of the money.More news: SNL Takes Dig at Alec Baldwin in Cold Open
It also said that the loans involved a company - Rock Holdings - based on the Isle of Man, which was impermissible under finance rules.
"The money came from Rock Services, which was a United Kingdom limited company".
Liz Bilney, a Banks associate who is also under investigation, added: "I run the group of companies where the money was from and we don't have any transactions that are from Russian Federation".
Mr Banks revealed he will be publishing bank statements on Monday that show "no money came in from overseas foreign sources".
"The money came from Rock Services which was a United Kingdom limited company". It doesn't make any money itself.
He told Sky News: "The £8m came from a United Kingdom company, the cash was generated in the UK".
Another £6 million was reportedly loaned by Banks on behalf of Leave.EU, with £2.9 million used on referendum campaign spending and donations to other groups.More news: New Mexico's record-shattering early voting, by the numbers
This would have made it an "impermissible" source of money under United Kingdom electoral law.
At the time Watson asked: "Did (May) ask the security services to investigate? It was generated out of insurance business written in the United Kingdom".
The "unprecedented" involvement of the NCA in the case was an important step because the agency was able to examine all financial records of Banks's businesses, including in areas outside United Kingdom jurisdiction such as the Isle of Man, said Mr Collins. 'I want to be absolutely clear about that.
"It's important that the investigation goes ahead as quickly as possible and that Arron Banks is investigated".
Richard Tice of Leave Means Leave told BBC Newsnight that "Remoaners" were using the investigation as an excuse to try and overturn Brexit.
"There are two issues here".
His funding of the Brexit campaign has been dubbed the biggest donation in British political history.More news: O'Rourke optimistic while casting ballot; Cruz confident after voting early
Both Bilney and Banks deny any wrongdoing, with the latter posting a flurry of tweets on Friday evening.