Our fiscal system actually discourages low-income parents from either forming or declaring a partnership, either married or cohabiting. It makes sense, if you depend on benefits for all or much of your income, to keep relationships "off the books". Tax credits, for example, are the same for two-parent and single-parent families, in spite of the fact that there is another adult to support in a two-parent household.
Housing policy also favours single parents. Social housing is allocated on the basis of "housing need" and single parents are more likely to tick the boxes that take you to the top of the list, such as low income and health problems.
In other areas of family policy, such as adoption, child support and access arrangements, married and single parents are treated in the same way. So why bother to make a public and legal declaration of your commitment, when it will give you no advantage?