Increasing numbers of people in work are finding themselves in poverty, according to a report published by the Joseph Rowntree Foundation.

The report highlights the growing incidence of well-educated people on the breadline because of a failure to find a job. The report charts the changes in recent decades in levels of poverty in Britain – and seeks to explain why, despite higher levels of employment and a more qualified workforce, there has not been more success in combating poverty. The Monitoring Poverty report calls for the government to "give up the belief that welfare reform" is the solution and focus instead on the phenomenon of in-work poverty.

The report cautions that simply increasing employment and pushing more people into university "may be part of the answer but they are no panacea … they may even create new problems".

The authors point out that people are becoming more educated – among 25 to 59-year-olds the proportion with university degrees has gone up from 4% in 1981 to about 25% in 2011. But it warns that 20 years ago 40% of those looking for work had no qualifications while just 6% had university degrees. At present, each group accounts for 17%.

"Although far more graduates have a job, graduate unemployment has soared," says the report, adding that Britain risks in the future creating a "better educated workless population".

"As more people go to university, having a degree moves from being an advantage in the job market to the norm. The number of graduates who are either out of work or doing jobs that require much lower levels of qualifications makes this clear."

It also warns that higher employment has been a "less effective antidote to poverty" because there has been a steady fall in the average hours worked per worker, down 11% over the last 40 years.

The result is widespread deprivation, with the number of people experiencing in-work poverty rising by a fifth in a decade to 6.1 million. By contrast the number of people in jobless households has remained steady at 5 million.

Instead of employment providing a route out of poverty, the foundation cautions that Britons are increasingly reliant on welfare to top up low wages, with the number of working families receiving tax credits rising 50% since 2003 to 3.3 million; employment is being concentrated in low-paid work, resulting in 4.4m jobs paying less than £7 an hour; and only a "willingness among workers to do fewer hours is keeping unemployment in check", with 1.4 million working part-time while seeking full-time work.

Although the numbers of poverty-stricken pensioners and children have dropped, largely from increases in means-tested benefits for these groups, the foundation warns that child poverty is projected to rise from 2.6 million in 2009 to 2.9 million in 2015 and that over the same period poverty among working-age adults without dependent children is projected to increase from 3.4 million to 4 million.

Chiding ministers for claiming that "poverty is about worklessness and welfare dependency", the report says that in fact "60% of children in low-income households have a working parent, the highest proportion in the history of these statistics".

The rise in poverty rates is largely due to stagnating wages and benefit cuts which the foundation says will result in lower incomes for some of the most vulnerable people in society.

"It is the poorest households that are the most at risk and even small changes to their benefits will dramatically reduce their income. As such these cuts to benefit spending cannot be seen as a good thing," says the report. "Large numbers of families are to be hit by a combination of different cuts. These overlapping effects are something to which government has paid little attention."

The foundation said the precarious position of the poor – who pass in and out of work – led to deep levels of insecurity. Julia Unwin, chief executive of the Joseph Rowntree Foundation, said: "The most distinctive characteristic of poverty today is the very high number of working people who are also poor. Many more people have experienced poverty since the downturn, cycling in and out of insecure, short-term and poorly paid jobs. Tackling poverty requires a comprehensive strategy, but overcoming the frail jobs market must be the starting point."

The report's author, Tom MacInnes, research director at the New Policy Institute, said: "Low wages cause families to struggle with the costs they face, trapping them below the breadline. Changes across five decades demonstrate poverty is not inevitable – reductions in child and pensioner poverty show that.

"But it is in-work poverty that is becoming the modern face of hardship, and at the same time support for working people is being cut. The high level of in-work poverty undermines any idea that better incentives to enter work, the centrepiece of universal credit, is some kind of cure-all."

The government pointed out that full-time employment was up 51,000 this quarter and the number working part-time had risen 49,000. A spokesperson for the Department for Work and Pensions (DWP) said more than 80% of people working part-time did so because it suited their needs.

The spokesperson said: "Our welfare reforms will improve the lives of some of the poorest families in our communities, with universal credit simplifying the complex myriad of means-tested benefits. It will make work pay – by allowing people to keep more of their hard-earned money as they move into work – and directly lift hundreds of thousands out of poverty altogether.

"Furthermore, for people who have been dependent on benefits for years, moving into work can seem a big risk. Universal credit will reward people who choose to go back to work by ensuring that they are better off in work than on benefits for taking that risk."