Families who rely on a fathers' earnings alone are at greater risk of poverty than other households, with average incomes stagnant for the past 15 years, according to analysis by the Institute for Fiscal Studies.
The IFS said that because the father works in most single breadwinner households, those families have not benefited from the relatively large increases in women's earnings since the mid-1990s.
Over the past two decades, growth in the earnings of working fathers has been "extremely slow", at 0.3%-a-year on average, according to the thinktank. In contrast, mothers' earnings have grown by more than 2% a year.
While the incomes of two-earner families are 10% higher than in 2002-03, the incomes of one-earner families have not changed over that period.
"With men's earnings growing so slowly over the last 20 years, it has become increasingly hard for families dependent on the father's earnings alone to keep up with other families," said Jonathan Cribb, a senior research economist at IFS and an author of the report.
The research, funded by the Joseph Rowntree Foundation, found that fathers in one-earner couples were less likely than other fathers to be in well-paid professional or managerial jobs. They were also increasingly likely to have been born abroad.
"These figures show that families with a single breadwinner are under increasing strain and have become much more vulnerable to poverty," said Helen Barnard, head of analysis at the foundation. "Relying on one earner no longer protects families from hardship. Balancing work and caring, and earning enough to make ends meet is an uphill struggle for many.
"Ensuring families can keep more of their earnings, driving up the number of good jobs through the industrial strategy and ensuring parents can access good quality and affordable childcare will help ease the strain," Barnard said.
The report said that a growing number of children living in families with one working parent were at risk of poverty. The proportion of children living with one working parent and one non-working parent in relative income poverty rose to 43% in 2015–16 – after accounting for housing costs – up from 33% in 1994–95.
The Treasury said the government had taken action to help working families. "Income inequality is now at its lowest level since the mid-1980s and our reforms to the tax system mean hardworking people are keeping more of what they earn.
A separate survey by the charity Grandparents Plus found that one in four mothers would have to give up work if they did not have help with childcare from their own parents. Only 7% of parents said they did not rely on their mother or father to have their children while they worked.