The Centre for Social Justice (CSJ) says that the number of lone-parent families is increasing by 20,000 a year and will reach more than two million by the time of the next general election in 2015.
The CSJ warned of a "tsunami" of family breakdown and accused the Government of a "feeble" response to the problem and of turning a blind eye to its commitment to promote family stability. Some of the poorest parts of the country are becoming "men deserts", the report found, because there are so few visible male role models for children.
One of the problems is the dearth of male teachers in primary schools. In England and Wales one in four primary schools has no male teacher, and 80% have fewer than three. The absence of fathers is also linked to higher rates of teenage crime, pregnancy and disadvantage, according to the report.
Christian Guy, director of the CSJ, said the human, social and financial costs are "devastating" for children and adults alike, yet the response from politicians of all colours has been "feeble".
Liverpool has one of the highest densities of fatherless households in the country, with eight of the top 20 areas within its boundaries, the report found. In the ward of Riverside there is no father in 65% of households with dependent children. In the Manor Castle ward of Sheffield 75% of households are headed by a lone parent, most commonly a woman. Riverside in Liverpool was second with 71%.
The report, Fractured Families: why stability matters, which is published this week, also highlights the cost of family breakdown - an estimated £46 billion a year, or £1,541 for every taxpayer in the country. This has risen by almost a quarter in the last four years, and is projected to reach £49 billion by the end of this parliament, the CSJ said.
The CSJ condemned the Government's lack of action in failing to stem what it called an "epidemic" of family breakdown. Mr Guy said: "There are many misguided reasons for such political paralysis. Some argue that it is no business of politicians to meddle in the personal family choices people make. Others suggest that rising family breakdown is just a modern process, an inevitable trait of human advancement. Others say family instability doesn't matter.
"This has to change. Our political discourse about family policy must mature. Family breakdown is an urgent public health issue. Backing commitment and setting a goal of reducing instability does not equate to criticising or stigmatising lone parents or those involved."