Police are investigating reports that the bank account details of 1,000 UK customers, held by Indian call centres, were sold to an undercover reporter.
In April, arrests were made over call centre fraud in western India
The Sun claims one of its journalists bought personal details including passwords, addresses and passport data from a Delhi IT worker for £4.25 each.
But, in a BBC interview, the worker named by the paper denied the claims.
India's top software body said India was a "trustworthy" location and would treat the claims "extremely seriously".
The National Association of Software and Service Companies said it would work with authorities in the UK and India to ensure criminals were "promptly prosecuted and face the maximum penalty".
"The problem is not unique to any single nation - it is one that affects us all - and each of us has a responsibility to take on the criminals," its statement added.
Meanwhile, India's information technology and communications minister said the government had nothing to do with the "freak" incident, and would step in only if legally required.
The Sun alleged the computer expert told the reporter he could sell up to 200,000 account details, obtained from fraudulent call centre workers, each month.
Details handed to the reporter had been examined by a security expert who had indicated they were genuine, the paper said.
The information passed on could have been used to raid the accounts of victims or to clone credit cards.
But, in an interview on BBC World Service radio, the worker said he had been asked to make a presentation about his company by someone described as an associate of the Sun's reporter.
He said the associate then asked him to give a CD to the reporter, but that he did not know what was on the CD and did not receive any payment.
'Reflect on decision'
Meanwhile, a police spokeswoman said officers were not yet aware of "the breadth of what we are going to be investigating".
"While the allegations made in the dossier are very serious, City of London Police would like to remind people that incidents of this kind are still relatively rare," she said.
Lloyds TSB, Barclays and the Woolwich banks said customer security was a top priority and they would be treating the Sun's allegations seriously.
HSBC said it was investigating the claims but that it was too early to say whether any of its details had been involved.
An Abbey spokesman said: "There is no evidence from the Sun story today that Abbey's customer data was involved.
Other banks including Halifax, the Royal Bank of Scotland, NatWest and Nationwide said they did not have call centres in India, so were unlikely to be affected.
The Amicus union said it had warned of the "data protection implications" of offshoring financial services.
"Companies that have offshore jobs need to reflect on their decision and the assumption that cost savings benefiting them and their shareholders outweigh consumer confidentiality and confidence," senior finance officer Dave Fleming said.
The allegations in the Sun follow the April arrests of former call centre staff in western India in April.
They were said to have obtained passwords and then after leaving the company transferred money out of customer accounts.