Ministers have been urged to overhaul the government's contract with the private firm Atos Healthcare, which carries out medical assessments for benefits claims, after auditors said the deal did not contain "sufficiently challenging targets".

Work capability assessments (WCA) carried out by Atos are used to make decisions about whether people are fit to work or are eligible for benefits. The company has conducted about 738,000 medical tests on benefit claimants in the past financial year. However, it has emerged that 40% of people appeal against the decisions – with 38% of those successful.

The Labour MP Tom Greatrex wrote to the National Audit Office (NAO) earlier this year urging an investigation to ensure the deal gave taxpayers value for money. On Friday the National Audit Office criticised the Department for Work and Pensions (DWP) for not seeking "financial redress" for delays in carrying out tests and noted that the department had only collected 10% of possible penalties triggered by poor performance.

Greatrex, a shadow energy minister, said: "This is a damning assessment of the failure of the Tory-Liberal government to get value for money for the taxpayer or properly hold Atos to account for the chaos and confusion at the heart of the work capability assessment. … "The taxpayer is effectively paying for this service twice – yet the government has failed to claw this money back from Atos," he said to reimburse the taxpayer. "People who are genuinely sick and disabled need to be helped, not hounded. The government must reflect on this scathing report and bring forward serious proposals for reform."

The assessments were first piloted in 2008 by the previous Labour government. However, the use of the tests have been vastly expanded by the coalition – and in May charities pushed for changes. Last month Professor Malcolm Harrington, who was appointed by the government to review the test, told BBC's Panorama that the assessment remained flawed and that as a result people who were genuinely unable to work would suffer.

He said: "There are certainly areas where it's still not working and I am sorry there are people going through a system which I think still needs improvement."

Atos has benefited hugely from outsourcing. This month it won contracts worth £400m to test whether disabled people should continue receiving benefits despite scepticism from many campaigners over its performance.

An Atos Healthcare spokesperson said: "We meet our obligations in delivering a complex and challenging contract. We have also been flexible with the department and implemented all the changes and recommendations from the Harrington report."

The DWP said Atos was not being allowed to underperform and a review of contractual targets was being carried out. The department has also twice agreed improvement plans with Atos Healthcare when processing times exceeded the target. This happened in 2009, under the Labour administration, and at the start of 2012.

Changes have been made to ensure feedback was received from tribunals to understand why decisions were overturned, the DWP said, and in many cases new evidence was presented at appeal that was not available when the assessment was carried out.

A spokeswoman for the work and pensions secretary, Iain Duncan Smith, said: "The contract has changed considerably since it was signed by the last Labour government – it continues to evolve as we have it under constant review.

"In 2010, the Work Capability Assessment was not working properly and since then we've substantially improved it. It is a complicated area but we are committed to making it a success to ensure it is both fair and accurate for the user and value for money for the taxpayer."