Children are healthier and more likely to grow up with a good education and get a good job if their biological father lives with them.
But there are no benefits when a stepfather moves into the family home, according to a pioneering study.
The discrepancy was drawn from records of the lives of more than 1 000 children born to single mothers in Britain at the turn of the millennium. The study by researchers from the London School of Economics checked on reports of the health, intelligence and social skills of the children up to the age of seven.
It said that when single mothers were supported by their offspring’s biological father the children were as likely to do as well as those of the stable families that were always headed by both parents.
But if a stepfather joins a family headed by a lone mother, then the children are likely to grow up with the same problems as children from families that only have a single mother.
The researchers found that the children were less likely to do well at school or keep a job, and more likely to have a teenage pregnancy or slip into crime.
The latest study is the first to use evidence from a large-scale survey to analyse the influence of stepfathers. It was based on reports provided by families to the Millennium Cohort Survey, which has been following the lives of nearly 20 000 children born across the UK between 2000 and 2002.
The researchers found full records on 1 169 families where children were born to a single mother but a man subsequently moved into the home.
The team, led by Elena Mariani, said that a large body of evidence argues "that children who grow up in a household with two married biological parents do better overall than those growing up with a single mother". But, they said, no one has considered what happens to the children when a man, either the biological father or another partner, moves in.
The team checked on the health of children up to the age of seven, their test scores on intelligence and "socio-emotional wellbeing". The study said that these indicate wellbeing in later life.
The researchers said they found that "consistent with existing evidence, children who were born to lone mothers belonged to a lower socio-economic group than the children who were born and grew up in families with two biological parents".
They said that when a biological father joined the family, children "fared better" and "did almost as well as children who have lived continuously in a two-biological parent household since birth".
But families that experienced a parental break-up or where a stepfather moved in "had outcomes similar to children of continuously lone mothers".
It said there were only small differences in the development of children in lone mother and in stepfather families.
The report added: "The benefits of improved resources and parenting input are being offset by the difficulties in adjusting to a new situation in the child’s home environment when a stepfather joins the family.
"The benefits of a father’s entry for children’s outcomes in different areas are clearest if the father is biological and the union is stable."
Campaigners for the traditional family said the results pointed to the need to encourage biological fathers to stay with their children and for couples to marry.
Laura Perrins, co-editor of the Conservative Woman website, said: "This report shows how important biological fathers are to their children’s development. It is not just father figures who matter but fathers."