The bank Egg has refused to back down in the row over its cancellation of the credit cards of 161,000 customers.
After a meeting with the Labour MP and former consumer affairs minister Nigel Griffiths, Egg said there would be no change in policy.
Egg had reviewed its 2.3 million credit card accounts after it was taken over by Citibank last year.
Some customers complained about losing their cards, but the bank said they might become a high risk in the future.
"The review was based upon a large number of variables and studied the level of risk inherent in groups of customers, rather then every individual," said a spokesman.
"So while some customers in that group may be up to date with their payments and have a good record with credit reference agencies and so on, the probability of them becoming a higher-risk customer in the future is higher than we wish to accept," he added.
Different patterns
The spokesman explained that although someone might not be in default on their card, the bank could tell that they might be heading in that direction in the future.
"The probability of these customers getting into trouble was higher than we would want to accept"
To detect this, he said, Egg looked at changes in the way customers used their cards, such as applying for more cards or changing their spending pattern on existing cards.
Egg denied that failing to make a profit from customers who always paid off their borrowings each month had been a factor in its decision to cancel the cards.
It pointed out that it still made money on them, because it received a fee for every transaction.
Repayments
A spokesman for Egg described the meeting between its chief executive Ian Kerr and Mr Griffiths as constructive and helpful, but said there would be no change in its decision.
"I expressed my strong concerns about the letters sent to customers, particularly since I felt that more information could have been provided," said Mr Griffiths.
"I have received an assurance that Egg will ensure that the credit record of these card-holders will not be affected, as long as they keep up their agreed repayments," he added.
The bank will consider any complaints from customers who feel its decision to close their accounts was unreasonable.
Customers whose cards are being cancelled will not be able to use them after the notice period.
But they will not be forced to repay any outstanding money in one go unless they want to.
They will still have the option to pay the minimum monthly repayment, or pay larger instalments until the balance is cleared.
Mr Griffiths has already complained to the Office of Fair Trading (OFT) about Egg's cancellation of the cards, although the regulator has yet to decide if it will investigate.
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