Fraudsters are now widely targeting existing bank account holders because credit is now harder to acquire.
The all-party parliamentary group on identity fraud said crooks are finding it more difficult to use fake identities to open new accounts. This is because of restrictions on credit driven by the ongoing credit crunch.
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The parliamentary group says there has been a fall in traditional forms of identity theft, including "application fraud", where people use stolen or false documents to open an account.
But the group says there has been a vast increase in cybercrime, where fraudsters use the internet and e-mail to try to access people's existing accounts.
One bogus email now in circulation pretends to be from HM Revenue and Customs. It asks recipients for their bank account details to receive a promised tax rebate.
Nigel Evans, chairman of the parliamentary group, said criminals were being forced by the credit crunch to focus on individual accounts which offer "a guaranteed financial resource".