By Louise Greenwood
BBC Radio 4's Money Box
The method used is fooling an increasing number of customers
E-mail scams have so far cost British banks more than a million pounds and there is concern the bill could rise as they become more sophisticated.
The Association for Payment Clearing Services (Apacs) confirmed the cost to the BBC's Money Box programme, and said the problem is getting worse.
Lloyds TSB, Nat West, and Barclays have all admitted that customer accounts have been accessed and cash stolen, but none would say how much was taken.
The credit card provider MBNA, which was the victim of a high profile e-mail scam last year would not even confirm whether its customers had lost any cash at all.
But Sandra Quinn of Apacs told Money Box the problem is starting to cost the banks significant sums:
"The losses now we think are over a million, and we know that figure is growing... It is something we are extremely concerned about."
This type of fraud is known as "phishing".
People are sent an e-mail claiming to be from a bank which asks the person to respond with their account details and password.
Fraudsters then use that information to steal money from the account.
When phishing began around 18 months ago, the e-mails were often crude, written in poor English, and with spelling mistakes.
However, the fraudsters - believed to be criminal gangs working in Eastern Europe - are now sending far more impressive e-mails, and copying the graphics and typeface from the banks' own websites.
This method is fooling an increasing number of customers.
Andrea from Cleveland had £6000 stolen from her account. She told the programme:
"You just feel so stupid. You feel that you have been taken in by a con that should have been glaringly obvious."
'Not significant sums'
The banks that do admit to the problem are keen to play it down, saying only a handful of customers have been affected.
Matthew Timms, Head of Internet Banking at Lloyds TSB told the programme:
"There have been frauds that have taken place on customers accounts. It is very small numbers that have been affected and it was not significant sums."
Meanwhile, the advice is never to respond to such an e-mail and if you are worried, contact your bank using a method you trust.
BBC Radio 4's Money Box was broadcast on Saturday, 24 April, 2004 at 1200 BST.
The programme was repeated on Sunday, 25 April, 2004 at 2100 BST.