Adam Perkins has now admitted that his claim "the higher the proportion of unemployed adults in a household, the greater the number of children - on average - that it contains" is true only if you exclude households that do not have any children.
This is, I am afraid, not how you calculate an average. It is roughly equivalent to saying that Manchester City would have scored more goals than Arsenal per match this year if you don't count the matches where they failed to score any at all. He also justifies this by claiming: "the government dataset from which it is taken states that households refers to those where at least one occupant is aged 16-64 and at least one occupant is aged 0-15.". This is flatly untrue, as anyone with the remotest familiarity with household data knows.
The source data is here:
Looking at the link, to my eye the relevant description is: "Out of the 20.7 million households (where at least one member is aged 16 to 64), in April to June 2015, in the UK, 11.6 million (55.9%) were classed as working, a further 5.9 million (28.3%) were classed as mixed, and 3.3 million (15.8%) were classed as workless." In other words, the extra requirement which Adam Perkins states “and at least on occupant is aged 0-15” is not referred to in these data.
Jonathan Portes concludes:
As the ONS clearly states, this data covers all households, with or without children, where at least one occupant is aged 16-64.