The government has admitted that it cannot tell how far changes made to the troubled tax credits system will have an effect on the level of overpayments – which now stands at £6bn.

The admission comes in the government’s response to a scathing report by the Commons Public Accounts Committee, released quietly just before the parliamentary recess.

A picture of ongoing crisis in the flagship programme emerged in the MPs' report, with continuing overpayments and a lack of basic information about payments, fraud and error levels.

The design of the tax credits system had caused some overpayments, but the committee noted: “There have also been unforeseen overpayments due to software errors.”

The tax credit computer system has been repeatedly hit by crises, contributing to overpayments to claimants totalling £6bn between 2003-04 and 2004-05. Since then the government has announced changes to the tax credit scheme, while a series of changes have been made to the IT system.

But in May the committee warned that HM Revenue and Customs “does not have complete information on the causes of overpayments and is uncertain about how far each measure will reduce overpayments.

In its response, the government said it was “ difficult to produce a reliable breakdown of the effect of each element” of the changes to the tax credits system introduced in the 2005 Pre-Budget Report.

This was because the different measures introduced in a bid to stem the crisis interact, the response says. HMRC was “therefore unlikely to be able to produce an analysis which it could include in its annual report”.

The response says the government “shares the committee’s desire to reduce substantially the level or error and fraud” in the system. It says it had set out how it would do this in a July report.

“The improved performance of the tax credits system has meant that fewer overpayments are being caused by IT or administrative error,” the response says.

This was shown by improvements to the accuracy of processing and calculating awards, which rose from 78.6% in 2003-04 to 97.7% in 2005-06.

But the government disputed the committee’s view that the internet system supporting tax credits was “deficient from the outset”, leaving it vulnerable to attacks by fraudsters. The system was shut down in December 2005 after sustained attacks.

The response document says the system was “always designed to be secure” and that security guidance from the government’s e-envoy was not issued until after the site went live.

“There is a trade-off between accessibility for customers and the need to protect the system against the risk of fraud. A balance has to be struck between putting in additional security measures and delaying the programme unacceptably,” the response says.

HMRC had monitored the risks until November 2005 when “new information came to light about what appeared to be a specific and unprecedented attack”, when it judged the balance of risks had changed significantly, and closed the system down.