Action for Children found that people in the UK incorrectly believe they will not be allowed to foster children due to a number of "myths".
With Fathers Day coming up on Sunday, the Office for National Statistics have released a selection of data on Dads.
Criminal records which date back to 1770 are being published online, including details of Victorian serial killers and habitual drunks.
A Department for Business spokesman described the current parental leave system "old-fashioned and too rigid" after a study found few fathers are taking additional paternity leave.
The spokesman said: "This is why we are introducing a system of shared parental leave from April 2015 so that fathers can take more leave if they want to in the early days of a child's life.
"We want to challenge the myth that it is the mother's role to stay at home and care for children".
TUC General Secretary Frances O'Grady said a "good gift" this Father's Day would be for ministers to increase statutory paternity pay rates and for employers to top it up for longer.
Ms O'Grady said: "Poor levels of financial support are preventing new dads from taking extra time off and are particularly affecting low-paid fathers who simply cannot afford to take leave.
"Extending paternity pay from two to six weeks and paying a better statutory rate would make a massive difference, as has been shown in other countries".
Few fathers in the UK are taking advantage of additional paternity leave, mainly because of the low statutory rate of pay they would receive, according to a report released today.
A study by the TUC suggests that of 285,000 men eligible to take up to 26 weeks leave, just 1,650 did so in 2011/12.
The TUC claims the low take up is because men cannot afford to live on the statutory weekly rate of £136 a week - which is rarely topped up by employers.
In contrast, most fathers take the first two weeks of paternity leave, which is usually topped up by employers, they added.
The Centre for Social Justice (CSJ) has condemned the Government's lack of action in failing to stem what it called an "epidemic" of family breakdown.
Director of the CSJ, Christian 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.
A report on family breakdown suggests the instability of cohabiting couples has fuelled the disintegration of families in the UK.
Since 1996, the number of people cohabiting has doubled to nearly six million, the Centre for Social Justice (CSJ) found.
The report, Fractured Families: Why Stability Matters, stated that cohabiting parents are three times more likely to separate by the time a child is five years old than married couples.
It also highlights the cost of family breakdown, which the CSJ said is estimated at £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 added.
The absence of fathers in British families is linked to higher rates of teenage crime, pregnancy and disadvantage, according to a report on family breakdown.
The director of the Centre for Social Justice, which released the report, said the human, social and financial costs of family breakdown are "devastating" for children and adults alike.
Christian Guy said: "For children growing up in some of the poorest parts of the country, men are rarely encountered in the home or in the classroom.
"This is an ignored form of deprivation that can have profoundly damaging consequences on social and mental development.
"There are 'men deserts' in many parts of our towns and cities and we urgently need to wake up to what is going wrong".
Some of the poorest areas of the UK are becoming "men deserts" because there are so few visible male role models for children, a report by the Centre for Social Justice (CSJ) suggests.
One of the problems is there are so few male teachers in primary schools, the independent think tank said.
It noted that one in four primary schools in England and Wales has no male teacher and 80 percent have fewer than three.
The report found that Liverpool has one of the highest densities fatherless households in the country, with eight of the top 20 areas within its boundaries.
In the ward of Riverside, there are no fathers in 65 percent of households with dependent children.
In Sheffield's Manor Castle ward, 75 percent of households are headed by a lone parent, most commonly a woman.
More than a million children in the UK are growing up without a father, according to a report on family breakdown.
The Centre for Social Justice (CSJ) claimed the number of lone-parent families increases by 20,000 a year and will reach more than two million by the next General Election in 2015.
The CSJ warned there was a "tsunami" of family breakdown and said the response from politicians has been "feeble".
It also accused the Government of "turning a blind eye" to its commitment to promote family stability.