The chairman of a key consumer body has called for changes in the way banks deal with customers allegedly involved in fraudulent activity.
Banks currently close customer accounts without explanation and refuse to discuss their decisions.
Adam Phillips, who chairs the Financial Services Authority's Consumer Panel, says current practices go against the rules of natural justice.
The banks say they are following anti-money laundering rules.
Radio 4's Money Box programme first highlighted this issue when it reported how a six-month-old baby girl had her account closed in error following an incorrect allegation of fraud.
Once an account is closed, fraud prevention agencies put a flag against the customer's name so they cannot normally then open an account with another provider.
Mr Phillips said: "You cannot find out what you're accused of, you cannot plead your case and you find yourself unable to open a bank account and nothing can be done about it. What's happening goes absolutely against the rules of natural justice."
"Fred", a 20-year-old student, had his account closed last year by NatWest.
In December he was on holiday in France, when he received a call on his mobile. "It was a man who said he was from NatWest.
"He said cheques had been paid into my account in error. He said I should leave the money alone, and correcting balances would appear and the money would move out of my account."
Fred assumed it was being sorted out, but when he returned home, his NatWest debit card was swallowed by a cash machine.
When he contacted his bank, he was told his account was being closed: "I was made to go to the counter and clear my account in cash. You feel like a criminal when you're marched over and marched out the door without being given any reason as to why your account is being closed."
The fraud prevention service CIFAS told him that beside his name was now an entry submitted by NatWest which said he had committed "first party fraud", which it described as the fraudulent misuse of a bank account.
Fred had no idea how this flag could have appeared. And as he could no longer access his bank statements, it was impossible for him to find out.
When he went again to his local NatWest branch to demand to see a list of transactions on his account, he saw that payments totalling about £9,000 he had no knowledge of had been paid in.
So he wrote to NatWest's fraud department saying the cheques had nothing to do with him and urging staff to investigate and clear his name.
In January, he received a reply from a member of NatWest's account closure team: "I have thoroughly investigated your complaint and following a review of your case, I can confirm that our decision to close your account remains the same.
"The bank has made a commercial decision to close your account. I cannot enter into further correspondence with you on this matter."
Fortunately, Fred then remembered the mysterious call he had received in France about payments made in error into his account.
Turning detective, Fred's dad tried to discover who had made the call by looking at the log of received calls recorded in his son's mobile phone. He managed to trace the number back to a branch of NatWest in Oxford.
Finally, when Fred contacted the branch about the call, staff admitted that someone in the bank had mistakenly paid in eight cheques totalling £9,000.
The branch staff there immediately promised to contact their colleagues in the bank's fraud department to sort things out.
It was not just Fred's NatWest account which was closed. HSBC also closed his current account after it saw the fraud flag. And when Fred tried to open an account with Barclays so he had some banking facilities, within a couple of weeks that was closed for the same reason.
NatWest said: "The branch made an error and paid in cheques to the customer's account. We did not pick this up in the first complaint.
"However, after he challenged the response to the initial complaint we picked up the error, overturned the decision, all credit default markers, and notified HSBC and Barclays. The customer was also offered £1,000 as well as reimbursements of costs £75."
Mr Phillips has asked the FSA to look into how widespread the problem is.
He also believes that fraud prevention agencies must allow innocent victims like Fred the chance to challenge their records. He said: "There has to be a discussion about an appropriate appeals procedure to decide whether the reporting is fair and whether it can be lifted."
BBC Radio 4's Money Box is broadcast on Saturdays at 12:00 GMT and repeated on Sundays at 21:00 GMT.