Mike O'Connor, chief executive of Consumer Focus, told Sky News: "Fee free banking is not necessarily good value if you don't get a good service."
But he added: "What must absolutely be avoided is customers facing the worst of both worlds; paying direct fees but still facing indirect costs, poor sales practices and customer service.
"Banks need to make big changes to regain customer trust. It will take a lot more than looking again at charging structures to address recent scandals in the industry."
Sir David Walker, who was appointed as chairman last week and will take up the role on November (Stuttgart: A0Z24E - news) 1, has set a 24-month deadline by which time he hopes the bank will be on firmer footing.
He told The Sunday Telegraph he agrees "in principle" with customers paying to use current accounts and the end of the free banking model.
He said that customers should pay as it might prevent mis-selling of financial products.
Sir David will replace Marcus Agius, who announced his intention to resign in the wake of the Libor-rigging scandal that left Barclays' reputation in tatters and sent shockwaves through the entire industry.
The former chairman of Morgan Stanley International will be tasked with steering the bank through the most turbulent period in its history, including appointing a new chief executive after the rate-fixing affair claimed the scalp of Bob Diamond.
Sir David told the Sunday newspaper that his highest priorities were appointing a new chief executive, reforming compensation and bringing about a changed culture.
He said he would like to speed up the process of "ring-fencing" so that the bank is functionally separated before the 2019 deadline set by the Government.
And he admitted that in principle he favours charging for bank accounts and services, and branded recent mis-selling episodes, such as interest rate swaps to small companies and payment protection insurance, as "the consequence of not charging for bank accounts".
Meanwhile, NBNK has confirmed news revealed by Sky News City editor Mark Kleinman that Sir David Walker is to quit the board of the banking start-up venture.