The controversy surrounding tax evasion strategies used by HSBC’s Swiss private banking arm will be reignited next week when Stephen Green, the former boss of the bank, faces questions in the House of Lords.

Lord Green, who left HSBC to become trade minister in 2011, will give evidence to the economic affairs committee at a one-off session on the culture of banking.

It will be the first time Green has appeared since leaving the government as trade minister in 2013 and since the Guardian and other publications revealed the strategies that HSBC’s Swiss arm used to help customers evade tax.

Green was chief executive and then chairman of HSBC from 2003 to 2010, the period covered by the leak of customer data about the banking arm, showing how it turned a blind eye to illegal activities of arms dealers and helped wealthy people evade taxes.

The so-called HSBC files, which cover the period 2005-2007, amounted to the biggest banking data leak in history, shedding light on around 30,000 accounts holding almost $120bn (£78bn) in assets.

The economic affairs committee, chaired by Clive Hollick, a Labour peer who used to run United Business Media, intends to ask Green about the Swiss operation and HSBC’s Mexican business, which was hit by a £1.2bn fine from the US authorities in 2012.

Imposing the fine, US regulators pointed to a “blatant failure” to implement anti-money-laundering controls in the bank’s Mexican operation that allowed local drug traffickers to deposit hundreds of thousands of dollars each day in HSBC accounts.

Hollick’s committee will also ask whether global banks are too large to manage and whether the policy of US prosecutors to issue multimillion-pound fines against companies, rather than prosecute individuals, is the right approach to improve the ethics and culture of banks.

Green will give evidence alongside Sir Win Bischoff, the veteran banker who is a former chairman of Lloyds Banking Group. Bischoff is currently chairman of the Financial Reporting Council. Green and Bischoff will also be asked about the bonus culture in the City of London.