Tribunal centres across the UK, including in Scotland, are also being forced to hold Saturday sittings to deal with disputed cases, politicians have been told.
Last night Labour called on the Tory-LibDem Coalition at Westminster to get a grip on the situation before it spirals “completely out of control”.
Almost four in 10 cases are currently overturned on appeal, a proportion campaigners say is unacceptable.
A series of written parliamentary answers has revealed the strain on the system. They show that centres around the country, including in Dundee, Hamilton, Cardiff, Plymouth and Wrexham, have been forced to hold Saturday sittings in recent months. Other centres, including Newcastle, South Shields, Leeds and Sheffield, are due to sit at weekends from this month.
In a parliamentary written answer, Chris Grayling, the Conservative minister, said 31 people had died while awaiting their appeal in the three years to last October.
Although there was no indication how they died, The Herald revealed earlier this year that two Scots who died while waiting to challenge their decision had died of the conditions that led them to apply for Incapacity Benefit in the first place.
The company responsible for assessing if disability or sickness claimants are fit to work is also struggling to meet demands to change its operations, the answers also show.
Atos, a French firm, is being paid £100 million a year by the Government as it seeks to cut the cost of incapacity benefit. But the company has faced growing criticism over its handling of the cases.
Following a report designed to reduce the number of incorrect assessments, Atos was told to put staff in job centres, where the final decisions are made. But Mr Grayling also admitted a shortage of resources meant that recommendation had yet to be implemented.
A telephone helpline was being introduced as an “interim arrangement until Atos is in a position to reintroduce the deployment of healthcare professionals in benefit centres”, he said.
Since October 2008, all those applying for a new benefit, the Employment and Support Allowance, which is designed to replace incapacity benefit, have been assessed if they are fit to work.
In April last year Atos also began reassessing all those currently receiving incapacity benefit, following pilots in Aberdeen and Burnley.
If trends continue, there will be 240,000 appeals over this financial year – a rise of 30% on the previous year, and at a cost of £60m in administration alone.
Tom Greatrex, the MP who obtained the information, warned the system was in chaos.
Mr Greatrex, the MP for Rutherglen and Hamilton West, has highlighted the case of one of his constituents who was deemed fit to work despite suffering from Parkinson’s and who eventually had his case overturned on appeal.
“The Tory-led Government must get a grip on this system before it spirals completely out of control,” he said.
“The rocketing cost of appeals, the huge rise in the number of Tribunal judges, and the introduction of Saturday sittings add up to one thing: the Work Capability Assessment is unfit for purpose.”
A spokeswoman for the Department for Work and Pensions (DWP) said under the older incapacity benefit system a higher proportion of decisions, 50%, had been overturned on appeal.
Atos last night referred inquiries to the DWP.