The family of a man who starved to death four months after his benefits were cut off has called on the government to reform the way it treats people with mental health problems when it assesses their eligibility for benefits.

Mark Wood, 44, who had a number of complex mental health conditions, died at his home last August, months after an Atos fitness-for-work assessment found him fit for work. This assessment triggered a decision by the jobcentre to stop his sickness benefits, leaving him just £40 a week to live on. His housing benefits were stopped at around the same time.

The Oxfordshire coroner, Darren Salter, said that although it was impossible to identify the cause of death, it was probably "caused or contributed to by Wood being markedly underweight and malnourished". He weighed 5st 8lbs (35kg) when he died; his doctor said his body mass index was not compatible with life.

Wood, of Bampton, Oxfordshire, was not told his housing benefit and employment and support allowance (ESA) had been stopped, and struggled to survive on the £40-a-week disability allowance that remained. He was reluctant to ask relatives for help and they were unaware his benefits payments had been removed until shortly before he died.

Concerned about his patient's condition, Wood's doctor, Nicholas Ward, wrote a letter for Wood to pass to the jobcentre in support of his benefits application, stating that he was "extremely unwell and absolutely unfit for any work whatsoever".

The letter, presented to the inquest, stated that his anxiety disorder and obsessional traits had been made "significantly worse" because of the pressure put on him by benefit changes. It continued: "Please do not stop or reduce his benefits as this will have ongoing, significant impact on his mental health. He simply is not well enough to cope with this extra stress. His mental and medical condition is extremely serious."

It was not clear whether the letter reached the jobcentre.

Dr Ward told the inquest the Atos decision was an "accelerating factor" in Wood's decline and eventual death, according to his family. Wood told housing association staff he was very distressed housing benefit had been cut off, and by letters about rising rent arrears and warnings from the electricity company his supply would be cut off. Many letters were unopened, so he was unaware he needed to visit the jobcentre to reapply for support, his sister, Cathie Wood, said.

He was a "sweet and gentle" person, she said. "He didn't deserve to die. He wasn't harming anyone."

Her brother had struggled with undiagnosed mental health issues all his life, which made it impossible for him to work. He was diagnosed with Asperger syndrome and obsessive compulsive disorder in his late 20s, and had an eating disorder and cognitive behavioural problems when he died. He was sacked from his first job because his employer said he was "unable to follow instructions".

"We worked for years to create a place for him to live safely. But that stopped when his benefits were stopped. He tried so hard to survive," Ms Wood said.

She is to write to David Cameron, who was her brother's MP, and to the work and pensions secretary, Iain Duncan Smith, to ask them to acknowledge that the system is not working for vulnerable people with mental health issues.

"I would like Iain Duncan Smith to stop talking about this as a moral crusade, and admit that this whole process of reassessing people for their benefits is a cost-cutting measure. I want and Cameron to acknowledge the personal costs of this flawed system. This is not just someone being inconvenienced – this is a death," Cathie Wood said.

She is angry Atos did not seek medical evidence from her brother's GP, and made the assessment that he was capable of preparing to return to work after a half-hour interview at his home. The Atos report concluded his mental state was "normal".

Cathie Wood wants the government to put new safeguards in place for vulnerable people when removing their benefits. She believes her brother was unable and possibly unwilling to convey the seriousness of his condition to the Atos assessors and should have had an advocate to support him.

"He was quite a proud person. He would have wanted to be seen as normal. He was desperate to get by as normal," she said. He was reluctant to call for help from his family. "He didn't want to impose on our mother. He wanted to survive without her help."

Wood's vicar told the inquest that he was a man of "dignity and integrity".

Between April and August 2013, Wood's BMI dropped from 14.1 to around 11.5. The inquest heard that a BMI of between 18.5 and 24.9 is considered healthy for a man. The inquest noted that he had developed an eating disorder.

"I am not saying that the government shouldn't reassess people's eligibility for benefits, but someone other than my brother should have been told that he had lost his benefits. This is an inappropriate process for people who are mentally ill. The Atos test is crude; they are not capable of making a judgment on complex mental illness in half an hour," said Wood.

Tom Pollard, policy and campaigns manager at Mind, said: "We were deeply saddened to hear of the death of Mark Wood. Unfortunately this tragic case is not an isolated incident. We hear too often how changes to benefits are negatively impacting vulnerable individuals, who struggle to navigate a complex, and increasingly punitive, system.

"We know the assessment process for those applying for employment and support allowance is very stressful, and too crude to accurately assess the impact a mental health problem has on someone's ability to work. This leads to people not getting the right support and being put under excessive pressure which can make their health worse and push them further from the workplace.

"We urgently need to see a complete overhaul of the system, to ensure nobody else falls through the cracks."

An Atos spokeswoman said: "Our thoughts are with the family of Mr Wood at this difficult time."

A DWP spokesman said: "A decision on whether someone is well enough to work is taken following a thorough assessment and after consideration of all the supporting medical evidence from the claimant's GP or medical specialist."

"Our sympathy goes out to the family of Mr Wood."

On Thursday, a government minister apologised after it emerged that the Department for Work and Pensions had written to a woman asking her to begin "intensive work-focused activity" although at the time she was in a coma.