Assuming, as is the convention, a threshold of 60 per cent. of contemporary median income as the measure of low income, then abolishing council tax for benefit units with annual income of less than £8,000 would:
have no statistically significant impact on the proportion of children in relative poverty;
lift around 60,000 pensioners before housing costs, or around 100,000 pensioners after housing costs, out of relative poverty; and
lift around 40,000 working age adults before housing costs, or around 20,000 working age adults after housing costs, out of relative poverty.
This is without taking account of any measures that might be taken in view of the reduced revenue flowing into local government.