During July and August, NatWest was receiving up to 640 complaints daily. [DQ Comment: All other banks are also finding similar levels of complaints.]
The money is being taken by payday loan middlemen, although customers are often unaware they have authorised a payment.
It is thought the regulator, the Financial Conduct Authority (FCA), is now looking closely at such activities.
In the meantime, the Financial Ombudsman has repeated a warning that consumers should be vigilant.
It said it had received 11,500 complaints about "rip-off" loan brokers since April, more than double the number in the whole of last year.
"In too many of the cases we sort out, no loan is provided and people's bank accounts have been charged a high fee, often multiple times," said Juliana Francis, the senior Ombudsman.
The money is being taken by online brokers, who offer to find consumers the best payday loan for them.
Typically they charge between £50 and £75 to do this, but fees can be levied up to three or four times.
Often customers are unaware they are going to be charged, or that they have given their consent for a payment.
NatWest said in one case, a man had taken out a £100 loan, but was charged £700 in fees.
It said the number of complaints was now down to around 250 a day, but it was worried that number might increase in the run-up to Christmas.
The bank also wants to see further action by the regulator.
"These are sophisticated organisations," said Terry Lawson, Head of fraud and chargeback operations at RBS and NatWest.
"They are resourceful, and more needs to be done at an industry and regulator level to protect customers who may already be in vulnerable situations," he added.
Some of the brokers involved in finding loans for consumers make their charges clear.
One of them is Loan Now, which gives a Californian postal address. "We charge a one-off loan-matching fee of £67.88," consumers are told.
But other sites make no initial mention of charges.
The BBC was unable to contact the sites, and it is thought that few of them belong to trade organisations.
Paul Williams, a director of Click4profit, which owns one site called Smart Loans, has previously said that most customers are satisfied with its service.
He also offered to issue refunds to anyone who is unhappy.
Meanwhile, the Competition and Markets Authority (CMA) is considering forcing brokers and lead generators to be much clearer on their websites.
It would like such sites to tell customers that they "are a broker, not a lender".
It said consumers are also unaware that, far from finding them the cheapest loan, many brokers simply sell their details to the highest bidder.
So it is also considering a compulsory health-warning, along the lines of: "We sell your application details on the best terms for us, rather than you."
The FCA is now considering applications from 5,200 brokers for authorisation.
They will decide next year which, if any companies, will be approved.
However, one industry source told the BBC that they are unlikely to give permission for the practice to continue.
"It is about to be killed, stone dead," he said.
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If you answered YES or MAYBE to any of these questions, then there are three organisation in the UK that can offer you free, completely confidential, personal and impartial advice on your money worries.
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PayPlan: Is a national organisation with approaching 20 years of experience in dealing with all kinds of financial situations, no matter how bad they are.
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Remember this forum is where you can still ask questions, where you talk to people who have been through financial problems themselves.
Want to talk to someone confidentially, without obligation and free of charge?
Abbreviations used in DQF
My advice is guidance only, if you want the law then consult a lawyer!
(c) All Spelling mistakes are my own design, infringement of them may result me sulking!