Financial Fraud Action UK (FFA UK) said it had seen a £36 million increase over the past year in crimes involving either online and phone banking, purchases made online and over the phone or criminals filling out fraudulent applications.
At least £7m of this has been put down to a scam known as "vishing", in which fraudsters claim to be from a bank or building society fraud investigation team, the police or another legitimate organisation such as a telephone or internet provider.
They attempt to get financial and personal information, which they can use to plunder the victim's account or commit identity fraud.
FFA UK said almost a quarter of people in the UK (23%) had received a cold call requesting personal or financial information, potentially meaning they could become a victim of the scam if the caller was not legitimate.
Four in 10 (39%) admitted they found it challenging to tell the difference between a genuine and fraudulent call.
The body estimates that around one in 25 UK adults may have already been duped in such a con and around four in 10 (43%) victims are estimated to be aged over 50 years old.
Almost a third (30%) of consumers received at least 10 cold calls per month. Older people were much more likely to receive calls they felt were dubious.