Nearly four out of 10 households with children, or 8.1 million people, live below an income level regarded by the public as the minimum needed to participate in society, according to new research commissioned by the Joseph Rowntree Foundation.

The number of those on less than the so-called minimum income threshold in 2012/13 was up by more than a third from 5.9 million in 2008/09, the charity says.

The research finds families headed by lone parents are under the greatest pressure, with 71% (2.3 million individuals) living below the required level, up from 65% (2.2 million).

The findings will fuel the debate about British economic growth, and whether it is feeding through to better living standards for most families. David Cameron will on Monday pledge to make full employment a priority if he wins in May.

The definition of minimum income threshold assumes a single person of working age needs an income of £16,284. It suggests in the case of a couple with two children, each needs to reach an income threshold of £20,400. It does not pretend to be a poverty measure, or act as a substitute for the government’s half-abandoned child poverty measure of the numbers earning 60% below median earnings. It is instead a definition of the income required to have not just food, shelter and clothes, but also to be able to be a participant in society.

The definition, reached in discussion with the public through focus groups, looks at what a household needs to be integrated in society and has been used in the past as a benchmark for the living wage.

It includes, for instance, the ability to pay for a week’s holiday in the UK, or a second-hand car for families with children. It assumes no cigarettes or visits to the pub.

Although the definition of the minimum income level may prove controversial with some, the trend towards more people falling below the threshold is significant. It reflects both the increasing cost of living relative to earnings and benefit cuts for households in and out of work.

The report finds that of the 3.7 million individuals living in single working-age households in the UK, 1.4 million lacked the income required for an adequate standard of living in 2012/13. This was 37% of single working-age households, up from 29% in 2008/09.

It suggests that among the 9.3 million individuals living in couple working-age households without children in the UK, 1.6 million lacked the income required for an adequate standard of living in 2012/13. This represents 17% of couple working-age households, up from 10% in 2008/09.

London remains the part of the UK where households face the greatest risk of being below the minimum income standard, influenced by high housing and childcare costs.

But in some other regions, notably Wales and the north-east, there has been a particularly sharp increase in this risk, to levels close to London’s. Households with members aged under 35 are now more than four times as likely to be below MIS than pensioners.

The report suggests that as employment rates for younger adults recover, their prospect of having an adequate income may improve. Working families with children, on the other hand, will continue to feel the effects of stagnating wages and benefit cuts because they are reliant on benefits to top up their low pay.

The report’s findings have been endorsed by Alan Milburn, chair of the Social Mobility and Child Poverty Commission.

He called the report “further evidence of the impact stagnating wages and fiscal consolidation is having on living standards of poor families. Despite very strong employment growth and record low worklessness, the number of people in families with children who are unable to attain what the public believe to be a minimum standard of living has increased by 2.2 million – more than a third – since the start of the recession, with the majority of the increase in working households”.

To tackle this, the next government would need to take action to recouple earnings growth with economic growth, he said. “Forging a new settlement to make Britain a living wage country by 2025 and ensuring that the working poor are protected from the impact of continued austerity in the next parliament.”

Mike Kelly, head of Living Wage at KPMG, welcomed the report saying: “Childless working households are the worst affected when it comes to low pay – and for them it’s getting worse, not better.

“For far too long, low income households have been struggling to make ends meet and for young people who are trapped in low-paid jobs, with little prospects, it’s an even bleaker situation.

“The fact remains that more than 5 million people are earning less than they need to live on. Too many families still struggle to afford the basics, meaning we face a scenario that, in 2015, should have long been consigned to the footnotes of history.”

Katie Schmuecker, policy manager at the Joseph Rowntree Foundation, said: “There has been a turnaround in who is suffering most as a result of the economic crisis and government measures to reduce the deficit.

“While last year’s monitoring report showed a sharp rise in young single people struggling to make ends meet, this year’s report shows a rapid widening of the gap between the incomes and costs of families with children.”

To alleviate the squeeze on working-age poor, JRF has called for:

• Reform of the markets for essential goods and services such as energy, financial services and transport, to ensure they provide good value for money and those on low incomes do not pay more than better-off households for services.

• National minimum wage rates to be set with regard to the changing cost of living and average earnings.

• Employers to pay the living wage where they can afford to.

• Changes to the design of Universal Credit so low earners keep more of the money they earn before benefits are withdrawn.