People who are fit and healthy are unlikely to have heard of the company Atos. But anyone who has had to apply for sickness benefits may find that the name triggers – according to one MP – a sense of "fear and loathing".

Atos is responsible for carrying out the government's drive to assess everyone claiming incapacity benefit, to decide whether they may actually be well enough to work. Atos staff are testing around 11,000 benefit claimants a week, to determine how ill they really are and whether they are eligible for benefit payments.

Since the last government launched a campaign to cut the number of sickness benefits claimants, the process has been controversial, with charities and politicians warning that vulnerable people have wrongly had vital payments removed.

On Tuesday a select committee will publish a detailed and critical report on the way the Department for Work and Pensions policy has been implemented, looking in part at the way Atos has carried out its contract to assess claimants. The work and pensions committee launched its investigation this year after many complaints about the testing process.

More than 400,000 appeals have been lodged against decisions not to grant the benefit since it was launched in October 2008, and 39% have been successful. The tribunals service has been forced to double the number of staff handling appeals, to accommodate the huge volume of complaints. The cost of tribunals is estimated at well over £30m a year.

Atos, a Paris-based IT company, is being paid £100m a year to carry out the work capability assessments (WCAs), allowing the government to phase out incapacity benefit and replace it with the employment and support allowance (ESA). The record of Atos Healthcare – a division of Atos – over the initial period of the policy's roll-out has been heavily criticised by disability charities.

There are two main areas of concern: unease about the government policy of retesting people's fitness for work, and alarm about practical hitches in the testing process delivered by Atos. Kate Green, a Labour MP who sits on the committee, said that while she was broadly supportive of the policy to help more people back into work, "the delivery has been absolutely disastrous".

Concern has been voiced beyond the select committee over the accuracy of the tests, the high numbers of successful appeals against the medical assessments, the facilities provided by Atos and the treatment of claimants by Atos staff.

For the past six months, Atos has been the focus of noisy protests by disability campaigners who have staged meetings outside its London headquarters, organised sit-ins at the medical assessment centres and sent protesters to picket Atos recruitment fairs. Protest banners declare "Atos doesn't give a toss" and "Atos Kills" – a reference to reports, highlighted by leading mental health charities, of people taking their own lives as a result of changes to their benefits. Those words have been painted on a wall near the company's London headquarters.

During the test, benefit claimants are interviewed by Atos staff – a mix of doctors and nurses – for between 20 minutes and two hours. Staff engage claimants in an often very relaxed conversation, gathering information about the medical problems, and calculating how capable the claimant is of performing simple tasks; a computer programme offers prompts to ensure that all the relevant material is inputted.

Staff can capture information in a sideways manner. The question: "Do you shop and cook for yourself?'' may be used as an indication of a claimant's mobility and competence. Atos staff award claimants between zero and 15 points (with 15 points indicating that they are too unwell to work), and send their reports to the jobcentre, where benefits officials make a final decision.

Charities have warned that glitches in the system have meant that many seriously ill people have been judged fit for work. A third have appealed, with 39% of decisions overturned by tribunals.

The tribunals service spent an estimated £22.15m on processing appeals between May and September last year. The service has had to double its capacity in the social security section to deal with the large number of appeals, recruiting an extra 170 paid medical panel members. The government accepts that the system has not run smoothly, and set up a review last year, headed by Prof Malcolm Harrington. His initial recommendations have been implemented by Atos. However, Harrington's review has not yet addressed all outstanding issues and will make further recommendations later this year.

During the work and pensions select committee hearings earlier this summer, MPs asked if Atos was penalised financially for inaccuracy. The company said it was paid per assessment, with no sanction if the decision was overturned on appeal. Anne Begg, Labour chair of the committee, responded: "That adds to the suspicion that you are a private company, you are driven by a profit motive, and the incentive is to get the assessments done, but not necessarily to get the assessments right."

Neil Coyle, director of Disability Alliance, said the government was paying the company to do the test, and was then footing the bill for reviewing flawed assessments. "It's like paying for a childminder to babysit, and then going home three times in an evening to make sure they are doing their job," he said.

A DWP spokesman said that if a decision were overturned, it did "not necessarily mean the original decision was incorrect", because new evidence was often produced, or "the tribunal weighs the original evidence differently".

MPs of all parties and from all parts of the country have found that the work capability assessment is a constant feature in their constituency mailbag. Labour MP Tom Greatrex was alerted to the issue last year when a constituent reported difficulties getting through to an Atos helpline.

Greatrex's office called the number 135 times before getting through. Although the phone service has subsequently improved, he said the "experience of both my constituents and my own office of the customer service provided by Atos has been entirely negative". He is concerned about the high levels of appeals, particularly now the system is no longer just testing new claimants, but has started retesting all 1.5 million incapacity benefit claimants to see whether they are eligible for the new benefit, ESA.

"The acceleration of the assessment process will mean that we end up with more and more mistakes being made. If that many people are winning their appeals, then it is grossly inefficient, apart from anything else," he said. A lot of his constituents felt that they were "being branded as skivers" and "demonised by the system", he said. The computer-led method by which Atos assessors work out how many points to award each claimant has also caused frustration, Begg said. "One of the big fears, and it was a common theme through all the evidence we got, was the mechanistic nature, the computer-based nature. I think a lot of your clients feel they are in the Little Britain sketch, where it says, 'The computer says no'," she told Atos staff at the hearing.

The Conservative MP Simon Hart was warned by Citizens Advice staff in Carmarthen that the test was causing many complaints. In a series of parliamentary questions, he established that 29,000 claimants who originally scored zero in the test were later granted the benefit on appeal.

"It seems that some people are not failing by a couple of points. They are failing completely and then going to tribunal and then passing completely. If it were missing by a narrow margin, you could understand that... there could always be a margin of error, but for some poor people the system is not working," he said. "The policy is a sound one, but it has to be fair and there does seem to be a group for whom it is obviously not fair." MPs also raised concerns about the numbers of assessment centres that were not well equipped to receive people with disabilities.Given the high level of concern expressed about Atos's current record, MPs wondered how the company was going to manage to deliver the "substantial savings" it promised when its contract was recently extended to 2015. Atos officials told MPs they would do that by "making the process more efficient".

Glenda Jackson, Labour, said she struggled to see how the company could improve its performance, as promised, and simultaneously cut costs. "How will it be possible with a reduced budget to improve and expand training?" she asked.

The Lib Dem MP Stephen Lloyd, asked Atos staff how they planned to improve their reputation. "It is not [an] exaggeration that, for x number of people in the UK who are currently going through this process, Atos is feared or loathed in equal terms."

Tom Pollard, policy officer with the mental health charity Mind, said it was often hard for charities to pass on their concerns to Atos. "It often feels like we are kept at arms length from Atos so they are not answerable as much as the DWP is," he said. Officials tended to respond that the problems highlighted by charities were "one-offs or isolated incidents" and this evidence tended to get "passed off as if they are the exception to the rule", he said.

"Often our experience suggests that the assessment is almost designed to ensure that it is catching out those people that might overplay things... to catch out scroungers. We often hear about people being asked slightly opaque questions... 'Do you watch Eastenders? ' And staff will extrapolate from that, that person will be able to sit repeatedly and reliably for 30 minutes. That's not quite straight from our point of view. It would be better to have an open conversation, where you don't need to cloak the questions," he said. "We don't believe that people overplay their symptoms or conditions; that doesn't line up with our experiences of the situation; they're more likely to underplay it if anything."

Some charities are also uneasy at the prospect of Atos being given further contracts for a new set of medical assessments that the government is to introduce in 2013 to test eligibility for the new personal independence payments (PIP), to replace disability living allowance.Richard Hawkes, chief executive of Scope, said: "They are responsible for the WCA and that doesn't work and so we would have great concerns if they became responsible for the PIP assessment as well."

The public's anxieties about Atos have been largely aired in blogs. Some disability campaigners have warned that by focusing anger on Atos, which is merely the company contracted to carry out a government policy, protesters are missing the point.When Atos (which is also responsible for IT at the Olympics) appointed athlete Steve Cram to be its UK ambassador for the 2012 Olympic and Paralympic Games, protesters turned their frustration on him, with a burst of angry online campaigning. The Disabled People Against Cuts group, wrote to him asking him "politely to reconsider his position", but say they have yet to receive a reply. Cram's agent said the athlete had not received a copy of the letter, although she had seen it online, and referred calls to the Atos press office.The company has recently taken legal action requesting closure of at least one website, which had invited people to post descriptions of their experiences of the medical assessment. Phil Lockwood who created a website, afteratos.org, earlier this year, was contacted by the company's lawyers advising him to take the site down.

An Atos spokesman said: "Atos Healthcare is focused on quality to ensure high standards are maintained. Customer satisfaction ratings for Atos Healthcare Professionals regularly exceed 90%." The company says it has introduced improvements in partnership with the DWP, including "improved consistency and quality of medical assessment and reports".

A DWP spokesman said the government was continuously improving the test, adding: "Prof Harrington is now undertaking a second independent review of the WCA, which will be published before the end of the year. As part of this he has launched a call for evidence and we would encourage people to respond."

Questions and answers: taking the test

A Guardian reader agreed to be accompanied to his recent work capability assessment. He has epilepsy and Asperger's syndrome and has been suffering from anxiety. He lost his job last year because of his ill health.

He was assessed by a nurse, who greeted him kindly and tried to reassure him about the process. The assessment started with an informal chat, and she asked how he had made his way to the assessment centre, clarifying whether it had taken more than half an hour. This was not just small talk, because the answers help build up a picture of potential fitness for work. The nurse asked questions about his diagnosis, but was also interested in his daily life.

"Do you go shopping?" "What happens if you have a fit when you're shopping?" "How long do you need to recover from it?"

"Do you do the cleaning at home?" she asked. "Do you do the cooking?" " Do you worry that you might leave the cooker on?" "Do you have pets?" "Do you have friends?" "Do you meet friends in cafes?" "Do you get the newspapers every day?"

Ability to cook and care for pets shows evidence of general competence, but claimants often find this roundabout form of evidence-building confusing.

She typed answers into the computer as she spoke, inputting his replies into the LiMA (logic integrated medical assessment) computer programme that processes the responses and helps translate the replies into a score between 0 and 15, with 15 being the point at which sickness benefit is recommended. She apologised for the noise of the keyboard being tapped, and for the fact that she had to take contemporaneous notes. After criticism about assessors looking at the computer rather than at the claimant, staff have been told to improve their eye contact.

After a while, the tone of the interview became much more business-like, the sympathetic murmurings stopped and the questions became more rapid. "Do you cry?" she asked, trying to gauge the seriousness of his anxiety. "Do you feel that life is not worth living?" "Do you feel that you can't on?" The replies (no) were typed in swiftly.

Two weeks later, the claimant was informed two weeks later that he was temporarily eligible for employment and support allowance, but would need to take part in "work-related activity" sessions.