The scam involved over 500 people including oligarchs and Russian criminals with links to the government and the spy agency, KGB.
Over that period, British banks including HSBC, the Royal Bank of Scotland (RBS), Barclays and Coutts reportedly handled over 1,900 transactions - out of 70,000 - worth nearly $740 million.
A further 373 operations are believed to have gone through US banks, for a total amount of $63 million.
"Barclays complies with the rules and regulations in all the jurisdictions in which it operates and has systems and controls in place to mitigate the risk of the bank being used to facilitate financial crime," a spokesperson for the bank said.
HSBC responded to the allegations saying: "The bank has systems and processes in place to identify suspicious activity and report it to the appropriate government authorities.
RBS said they were "committed to combating financial crime and money laundering in line with our regulations and have controls and safeguards in place to identify, assess, monitor and mitigate these risks."
According to The Guardian, while all major British banks will face questions over why they did not raise the alarm on suspicious money transfers, they only processed money that had already been laundered.
The newspaper reported however that American banks, including CitiBank and Bank of America, are the only ones that raise money-laundering concerns.