Hundreds of forms containing personal and confidential information about members of the public were lost by the Department for Work and Pensions (DWP).
Staff were told that 800 budgeting loan applications have been lost in transit between Sheffield and Newcastle.
In an email, DWP staff were told that customers had been querying the status of their missing applications.
In September, HM Revenue and Customs (HMRC) lost discs with the details of 25 million child benefit claimants.
Depots of courier company TNT are being searched for the latest missing parcels.
Interest-free budgeting loans are available to people who claim benefits such as income support so they can spread the cost of one-off expenses, such as household appliances.
Lee Rock, from the civil service union PCS, told BBC Look North the forms contained applicants' names, addresses, dates of birth, National Insurance numbers and bank details.
He said the loss of the forms was "outrageous" and urged anyone who had applied for a budgeting loan in recent weeks to contact the DWP.
In a statement, the DWP said: "Clearly we are extremely concerned that these payments have been delayed and we are striving to ensure no one is in hardship because of what has occurred.
"We are carrying out extensive checks with TNT to track down the whereabouts of the claims concerned."
The loss comes two months after HMRC lost discs containing the details of 25 million people.
The discs, which contain the entire child benefit database, were sent by courier to the National Audit Office in October - but they did not arrive.
Police are still looking for them.
And on Tuesday the Driver and Vehicle Agency in Northern Ireland said it had lost the personal details of 6,000 people.
The data was on two discs and went missing after being sent to the agency's headquarters in Swansea.