The action follows a settlement in the US last year where Visa and Mastercard agreed to pay retailers, including Asda’s owners Wal-Mart, $7.25bn (£4.7bn) in backdated fees.
It comes just days after the European Union proposed caps on the amount banks can demand for processing customers’ credit and debit card payments.
EU chiefs want to set a limit of 0.2% on debit card payments and 0.3% for credit cards.
The British Retail Consortium said retailers pay £850m a year to card schemes and banks to process card fees.
Helen Dickinson, BRC director general, said the proposed EU cap would save retailers £362m a year.