1. The California calculation includes state and federal income and employee share of federal payroll taxes; the UK site appears to include only income tax [see EDIT] (the UK has more complicated payroll tax rates, but each of the employee and employer share can be close to as much as the
combined US rate of 14.85% below the Social Security cap) [1].
2. The UK has much higher consumption taxes than the US (including California) with a 20% VAT and gas taxes close to $3/gallon, compared to (in California) a maximum of 10.25% sales tax and $0.725/gallon state+federal excise tax on gas.
[1] https://www.gov.uk/national-insurance-rates-letters
[EDIT: Actually, the UK calculation does include “National Insurance”, which is the payroll tax equivalent, but it is after the "total tax due" that the parent used for the comparison. With the employee share National Insurance payment included, the UK total is 30%, higher than the CA amount even before considering the impacts of higher consumption taxes and the higher employers-share National Insurance.]
