Consumer affairs group 'Which?' wants the new financial regulator to be held accountable for bank overdraft charges, often criticised for being too complicated to understand.
The government is in the process of replacing its Financial Services Authority (FSA) regulator with the Financial Conduct Authority by the end of this year.
The move comes after the FSA was criticised over its role in the 2007-08 banking crisis which led to Royal Bank of Scotland and Lloyds Banking Group being bailed out and part-nationalised.
Which? launched a campaign on Tuesday -- Watchdog Not Lapdog -- urging the government to ensure the new FCA is strong enough to tackle banks about overdraft fees.
It follows a survey conducted by Which? that found people paying a wide range of fees for unauthorised overdrafts.
It said mutually owned Nationwide Building Society charged the highest fees for customers who make one payment from their account while being overdrawn for two successive days in a month.
At 50 pounds, this was five times more than at the Lloyds-owned Halifax, Which? said.
HSBC and its First Direct offshoot charged the highest unauthorised overdraft fees on current accounts, at 150 pounds a month.
While the government has previously announced reforms to tackle unfair overdraft charges, they simply don't go far enough. It's extremely disappointing to find that bank charges are still too high, too complex, and impossible to compare, Which? Chief Executive Peter Vicary-Smith said in a statement.
It's essential the government gives the new financial regulator powers to limit these charges and to challenge their complexity.
The banking sector is dominated by the Big Four of HSBC, Barclays, Royal Bank of Scotland and Lloyds.
Last year, the FSA's banking regulator, Andrew Bailey, said it was unclear whether customers were being overcharged, but agreed on the need for greater fee transparency.
(Reporting by Sudip Kar-Gupta; Editing by David Hulmes)