Should Welfare be cut for single mothers?

In the UK, welfare isn't given out automatically if you are a single mother, only if you meet the criteria for receiving governmental help, i.e. don't have enough income to cover your costs. (Although the parents/carers of all children in the UK receive a small amount of child tax credits per child, regardless of income). Therefore, it would be stunningly unfair to cut the benefits of single mothers, just for being a single mother. What could she then do to cover her rent and feed herself and her family? There is certainly a poverty trap where the cost of rent and childcare is so high in some parts of the UK that parents struggle to earn enough to cover it, and so find that they make less money when they are working than when they receive benefits. This doesn't mean that benefits should be cut, however, but that wages should be raised and rents lowered. What is a disgrace is not single mothers but greedy landlords and employers who rely on government benefits to make up the shortfall.