Shadow work and pensions secretary Liam Byrne urged the Government to stop wasting taxpayers' money after uncovering figures which showed the estimated cost of tribunals hearing employment and support allowance (ESA) appeals rose from £21 million in 2009/10 to £66 million in 2012/13.
Mr Byrne said the Department of Work and Pensions (DWP) needed to "get a grip" after uncovering the figures in a parliamentary question to the Ministry of Justice.
The figures, disclosed by Mrs Grant, showed that under the coalition Government the cost to the courts service increased by £24 million - up from £42 million in 2010/11.
Mr Byrne laid some of the blame at the door of Atos, the company controversially contracted to run work capability assessments on behalf of the DWP, saying "more decisions are wrong than ever before".
Speaking outside the Commons chamber, he said: "Atos is now spinning out of control and it is costing the taxpayers millions to clean up the mess.
"DWP have got to get a grip of this fast before more public money is wasted."
Labour, citing House of Commons library evidence, claimed the increased costs since 2010 seemed "likely to be related to an increasing proportion of claimants appealing against a refusal of ESA, due perhaps to increased publicity and campaigns by third parties".
Mrs Grant acknowledged that a rise in the number of appeals was partly to blame for the increase in costs to the HM Courts and Tribunals Service (HMCTS). The total number of appeals, dealt with both inside and outside tribunals, has increased 66% from 279,000 in 2009-10 to 465,500 in 2012-13, Mrs Grant said.