Where a lone parent has just one pre-school child, the incentives to work longer hours are still "relatively low", the report claims.
Once a lone parent's youngest child has reached the age of 12, and is attending a secondary school, they should no longer qualify for income support on this basis.
In addition to rising inequality, Britain's lowly position in the poverty league table is accentuated by its particularly high share of children living in lone parent families and workless households.
The social care department said a single parent with an older child who is severely disabled will still qualify for income support on the basis that they are a carer, rather than a lone parent.
MPs over her plan to press ahead with the Conservative cuts in lone-parent benefit.
Any assault on family benefits (19%) will be tricky after last autumn's furore over lone-parent benefit.
The report says 28% of children in lone-parent families live in relative poverty, compared with 17% for those for "couple families".
Despite a decade of growth that has created 2.7m new jobs, the numbers claiming jobseeker's and lone-parent benefits have fallen only modestly, and those on incapacity benefit are virtually unchanged.
Since Labour's backbench revolt over last autumn's cuts in lone-parent benefits, the government has shown a propensity to hand out more money, helped by its bulging coffers amid an economic boom: more for families, pensioners, disabled people and child care.
But charities representing one parent families accused the government of "strong arm tactics" and said it would make life harder for lone parents by assuming that "government always knows best".
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