Ministers have apologised for a mix-up which led to bank and personal details of thousands of pensioners being sent to the wrong addresses.
The DWP has apologised for the mix-up
The Department for Work and Pensions (DWP) said it would try to trace all of those affected - as many as 26,000.
The Pensions Service chief executive has said banks are being warned and that no-one will lose out financially.
Pensioners have branded the mix-up "appalling". Some fear they could now be vulnerable to identity fraud.
Conservative MP Patrick McLouglin said the mistake was unacceptable and called on the department to "put it right".
Liberal Democrat work and pensions spokesman David Laws MP said: "Ministers should look into this mess to ensure that a mistake such as this is never made again."
A DWP spokeswoman said the letters, which were first received on Wednesday, were to inform customers what their weekly pension payments next year would be.
"Some of those customers received letters intended for someone else in that mailing," she said.
"As soon as we found out about it we acted immediately and launched an investigation."
The spokeswoman said she wanted to reassure the department's customers that all the letters would be traced, and no more letters would be sent out until the problem was sorted.
"We would like to apologise to customers affected. The department takes issues of customer security very seriously," she added.
The problem was caused when an extra letter was put into envelopes during a mass mailing of 11.8 million pensioners.
The service is writing to all those affected, providing pre-paid envelopes for wrongly-sent letters to be returned.
Alexis Cleveland, the chief executive of the Pensions Service, said banks were being contacted to alert them to the possibility some accounts could be susceptible to fraud.
She said pensioners were also being offered home visits to help them overcome any difficulties arising from the mistake.
"This is not what we would like to happen. It clearly isn't our finest hour," she told BBC News.
"I would not expect any customer that loses out financially because of our error to bear that cost."
The general secretary of the National Pensioners Convention pressure group, Joe Harris, said the mistake was "just the latest in a long line of mistakes".
"Last year they were asking pensioners to pay back overpayments of Pension Credit, now they're telling all and sundry other people's personal details."
Bevan Bullock, who received someone else's letter, said: "We're being warned on television about people going through your identity documents and so forth.
"The government are now giving them out willy-nilly."
One Derby resident reported receiving a letter with the bank account details of a person from Durham.
Another Derby pensioner told how a Leicester City councillor's national insurance number and bank account details were wrongly delivered.
Margaret Rothwell from Barnsley, whose details were sent to Bakewell in Derbyshire, said the "sheer inefficiency" was "appalling".
The department said any customers who received another person's details could call the Pension Service on 0845 60 60 265.