Andrew Mitchell, the social security minister, said the change would come into effect next week in the "extremely rare cases" where the CSA is at fault in sending a form to a person who is not the parent of the children in question. "This is to compensate for the possible upset and inconvenience caused by this error," he said in a written parliamentary answer.
One of the CSA's many problems since its launch three years ago has been a series of well-publicised mistakes which have threatened marriages because wives have opened letters from the CSA which were based on erroneous information.
Headlines such as "CSA blunder nearly ruined my marriage", over the story of Steven Sheppard, whose wife Janet opened a letter from the CSA, have embarrassed ministers.
According to the CSA two years ago, Mr Sheppard, the father of two girls aged seven and 12, also had a 10-year-old daughter by another woman. After the mistake was uncovered, Mrs Sheppard said: "I'm so angry. We had the biggest row of our entire marriage. In 13 years I've never once doubted Steven. But they destroyed all that trust with one letter."
In the last nine months for which figures are available, there were 28 instances where the CSA "may have been responsible" for wrongly identifying absent parents, a spokesman for the Department of Social Security said. This was an infinitesimal proportion of the 153,000 forms sent out.
The payment would not be available where the CSA acted in good faith, for example in response to malicious claims that someone had fathered a child.
The new rule forms part of a further package of reforms which have already stilled much of the fierce criticism of the CSA from aggrieved fathers.
Last year, travel-to-work costs were taken into account for the calculation of maintenance payments, and a limit of 30 per cent of the absent parent's disposable income set for maintenance.
Last week, a more thorough system of allowing "departures" from the rigid formula for calculating maintenance started to come into effect. Mr Mitchell also announced that interest would be payable on maintenance paid late because of delays caused by the CSA.
Yesterday, Mr Mitchell also announced that he would be acting on the criticisms made by William Reid, the parliamentary ombudsman. He will appoint an independent complaints examiner in the summer, as Mr Reid demanded last week.
Mr Reid said that one-third of the complaints he receives across all government departments concern the CSA.