The memos, obtained by the BBC, say the Department for Work and Pensions is struggling to deliver employment support allowance (ESA).
ESA was introduced in 2008 to replace incapacity benefit.
The government acknowledged there had been problems but said it was bringing in a new firm to do tests for ESA.
The documents – which include six memos written by civil servants and advisers – also say claimants face an average nine-month wait after assessments. The target is three months.
ESA is intended for people who are unable to work due to sickness or disability. Claimants undergo tests, called work capability assessments, before learning whether they are eligible.
The memos say that ESA “is not delivering more positive outcomes for claimants” than incapacity benefit did.
The payment’s costs are expected to rise by almost Â£13bn by 2018/19, the documents say, warning the increase is “one of the largest fiscal risks currently facing the government”.
The benefit is becoming a “long-term destination” for too many people, they say, and more people than expected are becoming eligible for it.
This is thought to be partly due to restrictions on jobseeker’s allowance leading to an increase in ESA claimants.
A key aim of the benefit is to get people off welfare and into work, but the documents say this appears to be happening less than under incapacity benefit (IB).
“Employment outcomes actually appear lower than under IB”, they say, and the “wider policy problems facing ESA will persist” despite the change in the company in charge of the assessments.
Earlier this month the government said more than 700,000 people were waiting for an assessment, blaming the delays on Atos, the private contractor currently carrying out the tests. Ministers say Atos had a backlog of 200,000 when the government came to power.
Atos, which has agreed to end its contract early, has said its staff have been “vilified” and abused for doing what was asked of them by ministers.
Mike Penning, the minister for disabled people, said: “We do have problems with the ESA assessment.”
He said it was “something we inherited” from the previous Labour government – “but we are doing everything we can to address [it] which is why I’ve negotiated Atos out of the contract and we’re bringing in a new provider so we make sure that we can have proper flow of the benefits coming through.”
Mr Penning said he did not recognise the comments about financial risk to the government.
ESA is “fit for purpose”, he said, adding: “It needs to evolve, it needs to change as we go forward and we need to make sure we get the right decisions – as in any other benefit – the right money goes to the right people and that’s what the taxpayer would expect us to do.”
Nearly two million people are currently claiming ESA, which entitles them to just over Â£100 a week.
Work capability assessments are carried out both on new claimants and those in receipt of incapacity benefit before they are moved to ESA.
Some of those deemed eligible for the payment are given regular interviews to help them find work, depending on their level of disability
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