Lady Grey-Thompson led the commission, which was backed by three charities. ITN

Nearly half a million disabled people and their families could lose up to £58 a week under the coalition's flagship welfare policy – cuts so deep that one in 10 disabled households with children fear they might lose their home, a commission led by the Paralympic gold medallist Lady Grey-Thompson has found.

Backed by three charities – Citizens Advice, the Children's Society and Disability Rights UK – the commission examined the impact on disabled people of the switch from the complex set of means-tested benefits to a single universal credit payment from next October.

The commission's report, based on surveys of 3,500 disabled people and their families, says about 450,000 disabled people could stand to lose out under universal credit once it is fully implemented. Many are likely to struggle to pay for basic essentials such as food and heating, it says.

Three groups are particularly at risk, according to the report: 100,000 disabled children stand to lose up to £28 a week directly; 230,000 severely disabled people who do not have another adult to assist them are at risk of losing £28-£58 a week; and up to 116,000 disabled people who work could lose about £40 a week as the disability element of working tax credits is subsumed into the new scheme.

The charities and the commission are calling for more cash to be injected into universal benefits for disadvantaged families. "When families who may be affected were asked about losing £30 per week in support for disabled children, they expressed widespread concerns about having to cut back on food or heating, and getting into, or further into, debt," the report says. "Around one in 10 families expressed fears that they could no longer be able to afford their home."

The government claims universal credit will "make work pay", but the commission says it found evidence that the changes could make it harder for disabled people to remain in work.

Grey-Thompson said: "The findings of this report do not make easy reading. The clear message is that many households with disabled people are already struggling to keep their heads above water. Reducing support for families with disabled children, disabled people who are living alone, families with young carers and disabled people in work risk driving many over the edge in future."

Labour has called on the government to postpone the introduction of universal credit by a year, arguing there are too many unresolved problems.

Liam Byrne, the shadow welfare secretary, said: "This report is another nail in the coffin for David Cameron's claims we are all in this together. The PM tried to hide it in the Commons, but this report lays bare the truth that he is snatching up to £1,400 from 100,000 disabled children yet offering a huge tax cut to millionaires. Disabled people and their families are being forced to pick up the tab for the government's shambolic mismanagement of our economy".

The government reacted sharply to the report, saying it was "highly selective and could result in irresponsible scaremongering". A spokesman for the Department of Work and Pensions said: "We inherited a system of disability support which is a tangled mess of elements, premiums and add-ons, which is highly prone to error and baffling for disabled people themselves.

"Our reforms will create a simpler and fairer system with aligned levels of support for adults and children. More importantly, there will be no cash losers in the rollout of universal credit. In fact, hundreds of thousands of disabled adults and children will actually receive more support than now, including paying a higher rate of support for all children who are registered blind."