The Department for Work and Pensions has lost the public purse £1.1 billion in overpaid benefits in the last year, because of failures to use historic data and systems to detect errors on claimants' forms.
It has also underpaid other claimants by £800 million, causing potential hardship to families.
The DWP was unable to detect the errors in part because it lacked the proper data, and was not able to establish patterns of mistakes being made which could have improved interventions - according to a report from the National Audit Office, the government's spending watchdog.
The news comes as DWP chief information officer Joe Harley is set to be promoted to the role of running the whole of Westminster's IT strategy, in the post of government CIO. He has carved £1.5 billion from operational costs at the DWP.
The NAO noted that the department had demonstrated "commitment" to tackling its own administrative errors, but said that efforts to tackle mistakes by benefits claimants had so far been "less evident". Claimant error was relatively common, it said, given the complexity of the benefits system.
Amyas Morse, head of the NAO, said the problem would only be resolved if the department develops a "coherent strategy supported by good information".
In spite of efforts to tackle its own errors over the last five years, by establishing a body called the Fraud and Error Council, the department had brought about "no discernible decrease" in incorrect payments owing to customer error.
"The department and its agencies have initiated measures to improve customer service and reduce customer error, but it does not yet have enough information to target these initiatives effectively," the NAO said in its report. "The Department does not know, for example, whether there are any common patterns that would enable it to target interventions more effectively across all benefits."
It added that the DWP also lacks "enough consistently measured data on the costs and benefits of its interventions".
The DWP said it was simplifying processes. It added: "Our new fraud and error strategy focuses on preventing error in the first place, as well as detecting and correcting mistakes when they do happen."