The proportion of people living in poverty who are in a working family has hit a record high, according to a report that shows rising levels of employment have failed to translate into higher living standards.

The Joseph Rowntree Foundation said that while paid employment reduces the risk of poverty, about 56% of people living in poverty in 2018 were in a household where at least one person had a job, compared with 39% 20 years ago.

Seven in 10 children in poverty are now in a working family, the charity’s annual UK poverty report found.

Single-parent families have been the worst affected by the trend of wages falling behind living costs, it added. Working single parents accounted for three in 10 households in poverty in 2018, compared with two in 10 in 2011.

The JRF’s executive director, Claire Ainsley, said the charity’s latest barometer of poverty in the UK revealed the scale of the task facing Boris Johnson’s administration if it is to “level up” incomes across the UK by narrowing the gap between the wealthiest cities and poorer regions.

“The new government has a historic opportunity as we enter the 2020s,” she said. “Past successes in recent decades show that it is possible for the UK to loosen the grip of poverty among those most at risk, but this progress has begun to unravel, and it will take sustained effort across the country and throughout the governments of the UK to unlock poverty.”

Amid concerns that the poorest receive worse healthcare and have the most insecure jobs, Ainsley said it was an indictment of recent government policy that the number of people in poverty across the whole workforce jumped from 9.9% in 1998 to 12.7% in 2018.

Labour accused the government of allowing too many people to remain trapped in low-paid insecure work and “all too often the social security system fails to give people the support they need”.

Frances O’Grady, the general secretary of the TUC, said: “The government must crack down on business models based on poverty pay and insecure jobs. Zero-hour contracts should be banned and the minimum wage must go up to at least £10 an hour right away.”

Approximately 14 million people are in poverty in the UK – more than one in five of the population, including 4 million children and 2 million pensioners, up by 400,000 and 300,000 respectively over the past five years.

A family is classified as being in poverty if it has an income of less than 60% of the median income for their family type, after housing costs. A family’s income includes earnings from employment, self-employment, state benefits and inheritances.

The report said people were more likely to be in poverty if they lived in certain parts of the UK, in a family where there is a disabled person or a carer, if they work in the hospitality or retail sector, or if they live in rented housing.

The worst-hit regions were London, the north of England, the Midlands and Wales, while the lowest poverty rates were found in the south of England, Scotland and Northern Ireland, the JRF said.

The charity was especially concerned about the rise in young people living with their parents, who in a previous era would have started to buy a house and start a family of their own, which it named “concealed households”.

Twenty years ago, 20% (2.4 million) of 20- to 34-year-olds lived with a parent or guardian. That proportion rose to 30% in 2018, affecting 3.9 million people, the JRF found.

The report describes in-work poverty as a “critical issue for our economy” and calls for action to reduce job insecurity, lower housing costs and increase earnings for low-paid workers.

The JRF said the introduction of universal credit, which rolls six benefits into one, did not help many low-income families because it required upfront payments for childcare before households were able to access state support.

A Department for Work and Pensions spokesman said: “Tackling poverty will always be a priority for this government. We know that getting into work is the best route out of poverty – and there are more people in work than ever before. Wages are outstripping inflation and absolute poverty is lower than in 2010.

“We know that some need more help, which is why we spend over £95bn a year on working-age benefits. Millions will see their benefit payments rise further from April and we’re also boosting the incomes of pensioners each year through the triple lock.”

• This article was amended on 20 February 2020. An earlier version said the proportion of people with a job who live in poverty went up for the third consecutive year in 2018 to a record high. This should have said the proportion of people in poverty who live in a working family went up in 2018 to a record high.