The last three months have seen a 40% increase compared to a year ago in identity frauds, where fraudsters use a victim's name, address or other information to steal money or attempt to steal it.
There were nearly 34,000 cases, affecting banks and their customers, but also phone companies and home shopping, according to the industry fraud body, CIFAS - which described the figures as alarming.
The numbers of cases where fraudsters took over people's accounts to try to take money increased by over 80% from the same quarter a year ago to 10,500 - and they were 16% higher than the previous three months.
Most of the damage is being done online, the result of spam emails, computer infections or carelessness, allowing scam merchants to gain access to personal details.
And there are instances of mail being intercepted and criminals sifting through the contents of rubbish bins to look for useful information.
In the majority of cases banks or other businesses will bear the initial loss from fraud, though the cost can feed through to higher prices.