But most homes in the UK are single family homes (66%) and women changed from having 2.4 kids on average in 1970 to 1.66 in 2021, so you would expect household size to fall.

Yes, and if the number of households stayed the same then they wouldn’t need more housing. But, that’s not what is happening.

So when they say things like this: “the UK’s homes-per-capita ratio actually exceeds the US’s.” they are ignoring the differences in household sizes between the two countries.