Quote from the original Policy Report -
"What Is the Relationship Between Marriage and Poverty?
Children living with single mothers are five times as likely to be poor as those in two-parent families. Some economists have attributed virtually all of the 25 percent increase in child poverty between 1970 and
1997 to the growth of single-parent families. But are single parents poor because they are not married, or
would they have remained poor even if they married available partners? CENTER FOR LAW AND SOCIAL POLICY, Brief 3, May 2003.
However, more recent research has shown that a lot of single parent families actually decide to stay single as the welare to work reforms discourage them from being part of a family unit (google Katheryn Edin for papers on USA studies and Gregg, Harkness and Millar for UK reports, which are more up to date than the one you quoted and actually relate this to present day UK welfare to work policies for Lone Parents).
So perhaps it has nothing to do with the size of the family and is more to do with the people concerned, the environment the children are raised and the values of the parent/s involved in the upbringing.