The government has been accused of “leaving the disabled behind” in its drive for greater employment, after it emerged that more than half of the households in which nobody works contain at least one adult with a disability.

A major report by the Resolution Foundation thinktank, whose executive chair is the former Tory minister David Willetts, suggests that the government must offer the same level of focus to people with disabilities that it has given to helping single parents overcome obstacles to work.

The report congratulates ministers of all political persuasions on reducing the total proportion of households where nobody works from 20.5% in 1996 to 15.4% in 2015 – a reduction of a quarter. The proportion of children in such households has fallen faster, dropping from 17.6% to 11.4%, the report says. The report adds that the rise in employment since 2010 has been “exceptional”, with more 18-to-69-year-olds in employment than ever before (71.2% in the third quarter of 2015). However, authors Paul Gregg and David Finch warn that more than half (54%) of the remaining households where nobody works contain at least one disabled adult – amounting to 1.6m families. This compares to just over one in 10 (11%) workless households being single parents (without disability), of which 64% have at least one child under five. Less than one in 30 (3%) are parents who are without disability.

The report suggests that the drive to get parents into work through tax credit incentives – which apply to people who work 16 hours or more – and improved maternity leave, must be replicated for those households where someone has a disability if the government is to achieve its goal of full employment.

“For disabled people, the extent to which the tax credit system provides a incentive to work may be outweighed by the barrier to work that disability can create,” the report says. “A person may struggle to meet the 16 hours requirement due to the nature of their disability, or in the case of a couple, caring responsibilities. The success of policy measures to boost parental employment provide something of a template when designing support for disabled people, although it is clear that the support in place has not been effective enough and a significant shift in thinking about the barriers faced by disabled people is required.”

The report, Workless Households, Children and Disability, based on an analysis of the Labour Force Survey and Office for National Statistics data, notes that, although the employment gap between individuals with a disability and those without narrowed by 10 percentage points between 1998 and 2009, in 2015 it is still 33 percentage points wide (46% to 79%).

It says: “There is still catching up to do. Unlike broader gains in employment, the increase in working among the disabled has not been evenly distributed across different household types. Worklessness has fallen most among couples where only one partner is disabled. Although the workless rate has fallen among households – single and couples – where all adults are disabled, the fall has been slower and largely reflects an improvement in the aggregate level of employment.”

Within households where both members have a disability the report finds that, where one member works, it is often the case that the other works as well. It found a particularly high level of worklessness among single disabled people: 59% in 2015.

David Finch, senior economic analyst at the Resolution Foundation, said: “In order to progress towards full employment – and to make further significant inroads in reducing worklessness – the government must now focus its attention on helping out-of-work disabled people.

“This will require a fundamental shift in policy, and should be a key focus of the upcoming disability white paper.”