Police investigating reports a call centre worker in India sold British customers' bank details have said such incidents are "relatively rare".
Over 75% of IT services outside the US are sourced from India
But the claims follow warnings that sending such work overseas was an "accident waiting to happen".
The Amicus union has predicted that 200,000 financial service jobs will be exported from the UK by 2008, taking every banking and personal finance customer's details out of the country.
"It is only a matter of time before a serious crime is committed, which ruins the reputation of the British financial services industry," said David Fleming, the union's national secretary for finance.
"'Offshoring' is an accident waiting to happen."
And accountants Ernst & Young warned that "given the volume of offshoring that is going on and the risks attached, there will be a major regulatory failing within five years".
Secret passwords were among the account details passed on in the latest incident, according to the Sun newspaper.
These could be used to raid victims' accounts.
But banks said their customers details are as protected in overseas offices as in Britain.
Passwords and Pin numbers are never seen in their entirety by any workers, the British Bankers' Association (BBA) said.
However, 17 people have been arrested in India already this year over alleged call centre fraud of nearly £220,000. Some of the suspects are alleged to have tricked customers into revealing Pin numbers.
Some security experts have questioned whether the call centres' cheap labour costs make them more vulnerable to corruption.
Paul Howard, managing director of data security firm DISUK, said: "The salaries paid to these people are not at the same level as in the UK.
"That means that if somebody wanted to ask them to do something fraudulent, the amount of money that might be offered would have more of an impact on their life."
He also expressed concern about "the speed at which these places are being put together".
"They are having to bring in great numbers of people - it must be more difficult to do background checks in a country like India," he said.
US firms outsourcing work were increasingly conducting their own checks of providers' security rather than simply accepting assurances measures were in place, Mr Howard added.
"I am quite convinced that hasn't been happening in the UK, with these call centres," he said.
Industry chiefs in India have responded to this year's arrests by proposing a voluntary nationwide database of call centre staff with security clearance.
BBA chief executive Ian Mullen said: "Bank staff are thoroughly vetted wherever that may be.
"With over a million people employed in the financial services and with any business, very occasionally a bad apple will slip through the screening process."
A spokeswoman for Royal & SunAlliance, which has predicted annual savings of £10m from basing some customer service operations and one of its seven call centres in Bangalore, southern India, agreed.
"Our view is that this is not about where a call centre is geographically based," she said.
"In any operation, from time to time, you get the odd bad apple.
"The issue is about how well you recruit, and how you monitor and manage staff to minimise the risk of this kind of situation occurring.
"We treat our operation in India in exactly the same way in terms of how we recruit and how we monitor it."
India's National Association of Software and Service Companies said in a statement: "Any case of theft or a breach of a
customer's confidentiality must be treated extremely seriously."
But it added: "The problem is not unique to any single nation - it is one
that affects us all."