Statistics released in the Social Trends study show that changes in the financial services industry have created criminal opportunities that investigating agencies have found it difficult to keep up with.
Back in 1981, before the massive increase in the use of credit cards, police in England and Wales detected 70 per cent of all frauds. But now most fraudsters get away with it and the clear-up rate for such crimes has tumbled to 48 per cent.
The battle against fraud is also being lost in Northern Ireland although Scottish forces have maintained clear-up rates at about 77 per cent.
Detection of thefts has plummeted in England and Wales from 38 per cent in 1981 to 24 per cent in 1997. Only one in eight thefts from vehicles is cleared up. Burglary detection has dropped from 30 per cent to 23 per cent in the same period.
Part of the explanation is that chief constables have concentrated resources elsewhere.
Detection rates for crimes against the person have increased over the past 16 years. Rapists now stand a 79 per cent chance of being caught, compared with 68 per cent in 1981.
But overall, the report says, detection rates are falling. "Clear-up rates fell between 1981 and 1997 in England and Wales: 38 per cent of offences were cleared up in 1981 compared with 28 per cent in 1997."