Some of the UK's top banks allegedly processed around £600 million in a multibillion-pound Russian money-laundering scam.
High street names including HSBC, the Royal Bank of Scotland, Barclays and Coutts are among those involved, The Guardian reported.
More than £16 billion and maybe as much as £65 billion was moved out of Russia between 2010 and 2014, the paper said.
Banking records detailing the scheme were reportedly obtained by the Organised Crime and Corruption Reporting Project (OCCRP) and Novaya Gazeta.
The documents detail around 70,000 transactions, including 1,920 totalling nearly £600 million that went through UK banks and 373 through US banks, according to The Guardian.
A Barclays spokesman said: "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.
"This includes risk-based systems and procedures to monitor ongoing customer activity, which we constantly review, and procedures for reporting matters to the relevant law enforcement authorities as appropriate.
"In addition, through a number of industry initiatives, Barclays partners closely with global law enforcement in the fight against financial crime."
A spokesman for HSBC said: "The bank has systems and processes in place to identify suspicious activity and report it to the appropriate government authorities.
"This case highlights the need for greater information sharing between the public and private sectors, each of whom holds important information the other does not."
RBS said: "We are 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."
A UBS spokesman said: "UBS applies a robust money-laundering prevention framework across its business operations globally, consistent with locally applicable regulations."
Shadow chancellor John McDonnell said: "This scandal needs to be investigated in full by the National Crime Agency, and the Government must ensure they have all the resources and support needed. Britain cannot be a haven for the criminals of the world who are looking to hide their money.
"It's deeply disappointing that there are British banks involved in yet another banking scandal as the actions of a few shouldn't overshadow the hard work of the thousands of employees in the sector who will have had nothing to do with this case.
"But it appears that some of these big banks haven't learnt the lessons of the past, and are clearly not doing enough to clamp down on financial crime and money laundering."