The Government has been accused of failing to ensure that single-parent families are treated the same as married couples.
The One Family support group says it wants changes to the Constitution to provide protection to all families and not just those based on marriage.
However, it says a "systematic problem" exists whereby single-parent families are more likely to be deprived of basic legal, economic and social rights than their married counterparts.
It says one-parent families are three times more likely to live in poverty, have lower education levels and have more difficulties accessing housing and other services.