Trade minister Lord Green is under intense scrutiny after it emerged that HSBC continued to operate hundreds of accounts with suspected links to Mexican drug cartels, even after Green and fellow executives were told by regulators that HSBC was one of the worst banks for money laundering.

The revelations, contained in a US Senate report, raise further questions about Green's stewardship of the bank and come as he prepares to play an important role at the Olympics by using the Games to secure contracts for British business.

Green, chief executive of HSBC between 2003 and 2006 and executive chairman from 2006 to 2010, has declined to comment on the report. Last night Labour shadow Treasury minister, Chris Leslie, wrote to Green, who is in the running to become the next governor of the Bank of England, demanding to know when he became aware of the problems raised in the report and the steps he took to remedy them.

Leslie writes: "It is a matter of significant public interest that you also have the opportunity to explain what, if anything, you were aware of during your time at the bank."

The Senate report quotes emails, copied to Green, that created alarm in the higher echelons of the bank. They show that in 2005 Green was alerted that HSBC had potentially breached sanctions relating to Burma and that its Mexico arm had fabricated its anti-money-laundering activity. More damningly, evidence is emerging that HSBC's lax controls continued to allow money laundering and other dubious transactions even after Green and his colleagues were made aware of the problems and pledged to take action.

In February 2008, Paul Thurston, HSBC Mexico's chief executive, warned the bank's group chief executive, Michael Geoghegan, that the country's banking regulator, CNBV, and its financial intelligence unit (FIU), had unearthed "multiple compliance concerns".

An email copied from Geoghegan to Green soon after noted: "This is most disturbing and we will need to have the most thorough of investigations." In a follow-up email, copied to Green, Thurston said that the FIU was deeply concerned about money laundering at the bank. "HSBC has historically, and continues to have, a worse record than the other banks, so we have become a focus of attention," Green was informed. "The new head of the FIU has told us that his staff have told him that HSBC has been the most difficult bank to obtain accurate and timely data from for the past four years."

Despite these concerns, all 675 HSBC accounts that the CNBV suspected of money laundering, and had demanded that the bank close, remained open months later, in December 2008. The Senate report also said Green was briefed personally on HSBC's role facilitating transactions for Iranian banks and companies. Such transactions were subject to strict regulations imposed by the US Office of Foreign Assets Control, which enforces American sanctions.

HSBC had installed a computer system to identify payments involving Iran so they could be vetted. But HSBC's US arm, HBUS, had concerns some of the Iranian transactions were not being identified. Green demanded action. On 20 June 2005, David Bagley, HSBC's head of compliance, who has now resigned, noted that Green wanted confirmation that the "agreed arrangements in relation to Iranian payments had been put in place". Bagley confided in a colleague that he was unable to give that confirmation and the Senate report found: "The vast majority of the Iranian transactions… were sent… without disclosing any connection to Iran."

In 2010, HSBC hired an outside auditor, Deloitte, to identify and review "Office of Foreign Assets Control sensitive transactions" at HBUS between 2001 and 2007. It identified that the bank had processed almost 25,000 transactions involving Iran and assets in excess of $19.4bn. The majority were undisclosed transactions that should have been identified and vetted. On 24 September 2007, HSBC group compliance issued a group circular letter announcing the bank's decision to exit Iran. But internal bank documents show that every month hundreds of Iranian transactions continued to surface at HBUS during 2008 and 2009.

Former Lib Dem Treasury spokesman, Lord Oakeshott, said: "Unlike Bob Diamond, Stephen Green was a thoughtful banker in holy orders. But if even he couldn't stop these scandals, banks like HSBC and Barclays aren't just too big to fail, they are clearly too big to control." HSBC has apologised and has said reforms have now been put in place.