The average cost of the theft was £3,039, and six percent claimed to have lost more than £10,000.
"Identity theft is a very serious problem and one that is getting much worse, so we all need to take greater care in protecting ourselves," said Donald MacLeod, credit card manager at Sainsbury's Bank.
"This could involve having a policy in place to protect against this crime, but it should also involve taking steps to reduce the chances of ID thieves being able to steal your personal details.
"Research shows that around three-quarters of household waste contains at least one item which could assist identity fraudsters."
London and the South East top the list of victims of fraud, with 16 percent of respondents saying they had suffered, compared to just four per cent in Scotland.
A report by CIFAS, the UK's fraud prevention service, estimated that ID theft was up 500 percent since 1999.
Sainsbury's Bank used the research as a backdrop for the launch of its own identity theft insurance. This would provide regular credit checks for customers, a dedicated team to help victims and up to £10,000 reimbursement for lost time.
However, the payout covers the cost of the identity theft and not the losses. These are automatically reimbursed once the bank has satisfied itself that fraud has taken place.