The National Autistic Society has warned the Government it must learn from the mistakes made on work benefits before it alters disability payments.
The performance of private company Atos in carrying out 738,000 face-to-face medical tests on benefit claimants has been questioned by the National Audit Office.
Earlier this month the government announced that Atos and Capita won the contracts to run a new work-capability check for disabled people.
The assessments, which will see Personal Independence Payments replace Disability Living Allowance, will start next year. Up to two million people will need to be assessed for PIP.
The NAO said DWP had failed to penalise Atos for "underperformance" or set appropriate targets.
Labour MP Tom Greatrex said that the contract is worth £112m a year to Atos.
"At the same time, through the Tribunals Service, the appeals are costing about £60m a year so effectively we are paying twice to try to correct the mistakes in the initial assessments or the process that leads to the assessments and decisions," he said.
Mark Lever, Chief Executive of The National Autistic Society, said:
"From day one, there have been significant concerns with the way the Work Capability Assessment works for people with autism.
"WCA has not only wasted money but caused untold distress for many thousands of legitimately disabled people.
"The Government must listen to the watchdog’s criticisms and act on them ensuring that they learn from the shortcomings of the WCA when introducing PIP.
"PIP needs to be a genuine strategy to improve the current system and not simply an attempt to save money.
"When the right support is not in place, people with autism often go on to develop more significant health problems costing the Government far more in the long-term.
"The government must ensure the way they outsource these vital disability benefit assessments is fair and fit for purpose, otherwise they risk failing thousands of those most in need."
Work and Pensions Secretary Iain Duncan Smith said:
"In 2010, the Work Capability Assessment was not working properly and since then we've substantially improved it.