A family relying on the father's earnings alone has an average income no higher than it was 15 years ago, according to analysis by the Institute for Fiscal Studies (IFS).
The research, funded by the Joseph Rowntree Foundation (JRF), said that because it is the father who is working with most one-earner families, these households have not benefited from relatively large increases in women's earnings seen since the mid-1990s.
Over the last 20 years, growth in the earnings of working fathers has been "extremely slow", at 0.3% a year on average, while mothers' earnings have grown by more than 2% a year, the IFS said.
It said: "As a result, it has become increasingly difficult for families where only the father is working to keep up with other families.
"This matters: around a quarter of children live in a one-earner couple family - around the same proportion as 20 years ago."
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, the analysis covering Britain found.
The research took into account the impact of inflation as well as calculating incomes from any benefits and wages after tax.
The IFS said fathers in one-earner couples are less likely than other fathers to be in well-paid professional or managerial jobs. They are also increasingly likely to have been born abroad.
Couples with younger children, and with more children, are more likely to have only one parent in work.
The IFS said 43% of children living with one working parent and one non-working parent were in relative income poverty in 2015-16, after accounting for housing costs - up from 33% in 1994-95.
Andrew Hood, a senior research economist at IFS and another author of the report, said: "Boosting the incomes of large numbers of families dependent on fathers' earnings may well be challenging.
"The vast majority of the fathers are already working full time, most of the mothers are not actively seeking paid work, and increases in in-work benefits targeted at the group would be likely to further weaken the financial incentive for those families to become dual earners.
"But increasingly it is a challenge that governments wanting to improve the living standards of low-income children should be considering."
A Treasury spokeswoman said: "We want to build an economy that works for everyone.
"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.
"Increases to the personal allowance have taken millions out of income tax altogether and reduced tax bills for some of the lowest earners by £1,000 a year."