US federal budget is 23% of GDP, while UK is 44% of GDP. You can't compare fractions of the fractions directly. (Total spend is something like 11% vs 18% GDP.)

Sure it's difficult to compare - but from your figures - the 11% is UK and the 18% is US ( total spend )?

With the UK spend roughly 80:20 government:private and the US spend about 50:50.

So as percentage of GDP government spend is about the same percentage of GDP but the much bigger private spend in the US what makes the difference.