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At least 35,000 people applying for sickness benefit are waiting longer than 13 weeks, the Department for Work and Pensions (DWP) has admitted.

DWP officials are privately blaming the backlog of employment and support allowance claims on French firm Atos, which carries out medical assessments.

Atos Healthcare said it had recruited additional staff and extended opening hours in response to the situation.

One member of DWP staff described the situation as "in meltdown".

Employment Minister Chris Grayling said there were "probably about four months behind where we would wish to be and we're in the process of clearing the backlog".

He said the backlog was down to the "transitional impact" of changes being made to the medical assessment, .

Employment and Support Allowance (ESA) replaced incapacity benefit and income support on incapacity grounds for new claimants in 2008.

ESA is paid to people who are unable to work because of illness or disability, and can provide support for those who are able to do some form of appropriate work.

The face-to-face medical appraisals on claimants are known as work capability assessment, and are meant to take place during a 13-week first phase of a claim - during which a basic rate of benefit is paid.

If the assessment determines a person's ability to work is limited, a second main phase of a claim starts from week 14 - from which time an additional amount is paid on top of the basic rate.

According to the DWP's own research, 35,000 people who put in their claim before May last year are still waiting for a medical assessment to determine whether they should receive the benefit. That is one in five claimants, when withdrawn claims are stripped out.

The number of people who have put in new claims in since May and are waiting longer than 13 weeks for a decision is not known.

Shadow employment minister Stephen Timms said the backlog of ESA claims was damaging the government's flagship employment initiative, the Work Programme.

In December, the DWP reduced its estimate for the number of people on ESA joining the Work Programme, which helps people on Jobseeker's Allowance or ESA to find a job.

"It is quite clear that the number of people on ESA being referred to the Work Programme is much less than expected and it appears that's because of delays in getting ESA decisions through," said Mr Timms.

"People out of work with health problems should be getting help to find a job and at the moment too many are not."

Mr Grayling said Labour was trying to "make a bit of beef" by linking the backlog of new ESA claims to the Work Programme.

The backlog is the latest problem for the DWP and Atos, which is paid £100m a year to carry out the Work Capability Assessments.

Since ESA was introduced, Atos has made a high number of incorrect medical assessments - about 40% of claimants initially turned down for the benefit are granted it on appeal.

Atos Healthcare said in a statement: "Following recommendations from the Year 1 Harrington Report, the Department for Work and Pensions made improvements to the format of Work Capability Assessment, which has increased the average time of the assessments.

"Atos Healthcare together with the DWP identified very quickly that they would need to respond to this change and recruited additional staff and extended opening hours to ensure that delays are minimised while every customer receives the individual time they need."