The Driver and Vehicle Licensing Agency (DVLA) broke data protection rules when confidential documents were sent to the wrong motorists, it has been claimed.
The DVLA at Swansea is conducting an investigation
The agency sent 1,215 questionnaires, including dates of birth and motoring offence records, and about 100 went to the wrong addresses.
The National ID Theft Assistance Centre said the DVLA had breached the Data Protection Act 1998.
The DVLA said "human error" had led to the "isolated incident".
Barry Stamp, managing director of the assistance centre, which helps victims of identity theft, said the DVLA should not have sent out personal information on a questionnaire, but it would not suffer any consequences.
"For many government departments there's very very little chance of any fines being imposed or anyone brought to book or indeed even the information commissioner making a spot check on that particular department," Mr Stamp said.
"There's simply no responsibility, so therefore it tends to be a lackadaisical approach to data generally."
The DVLA said all 1,215 drivers who were sent the questionnaires were being contacted to advise them of the error, apologise and discuss its implications.
The drivers had been contacted as part of a routine DVLA survey, it said.
The agency said notes had been placed on all 1,215 records on its database to prevent any fraudulent activity being attempted on that record.
It is holding an internal investigation and said it had sought advice from the police regarding any risk of identify theft to customers and had also contacted the information commissioner.
DVLA chief executive Noel Shanahan apologised and said it was in the process of contacting customers who have been affected.
"We have initiated an internal inquiry to establish exactly how this error occurred and to identify any changes in procedures that may be necessary," he said.
Mr Shanahan said that the error first came to light on Wednesday when the DVLA received calls from customers who had received envelopes in error.
Some of the 1,215 customers had the right information but others had their name and address on the front but the details of others inside, he said.
"We don't yet know exactly how many have got the wrong information but we know that some of them have," he said.
"This was definitely a human error.
"About 100m letters leave the DVLA every year. We have a very structured process and what happened in this isolated incident is that we didn't follow that particular process and we are now investigating as to why."
Conservative leader David Cameron, on a visit to south Wales, said: "It is extraordinary we've just had one example after another of government slip-ups on this issue of data."
"What we're seeing is systemic failure, there's something wrong with the systems in place that means it's happening again and again," he added.