Supporting good parenting
A small proportion (£100?) of each parent's BI should be earmarked as dedicated to the upkeep of each child.
If a child is taken into care, or moved from the care of one parent to another, not only should the child's BI transfer to the carer, but that small proportion of the failing parent's BI should too.
Single mothers would be invited to declare the father of their child. The state would fund DNA tests for those fathers who contest the claim. But for those who refuse the test or who are proved to be the father by the test, a part of their BI would transfer to the mother (or carer) as a contribution towards the care of the child.
Even feckless fathers with no earnings would thereby have an incentive to try to avoid fathering children that they were not prepared to care for, and would be driven to try to earn more the more children they father. That would be a marked improvement on the current situation where potential claims on earned income and withdrawal of benefits provide a strong disincentive for feckless fathers to find employment or take responsibility for children. The current arrangements create a vicious circle of deprivation where successive generations have become experts at exploiting the benefit system rather than learning useful skills for employment, and have strong incentives to avoid supportive family structures. Like so much else, the proposals of the mainstream parties would not meaningfully change these perverse incentives.
The transfer of this portion of the BI under these circumstances is additional to, not instead of, any decisions of courts on support from one partner to another amongst more affluent, separated parents.