To clarify something, in the UK there are two main deductions on personal income - income tax and National Insurance. National Insurance doesn't pay for healthcare, it pays for things like state pension and other support benefits - https://www.gov.uk/national-insurance/what-national-insuranc.... The National Health Service (NHS) is funded through taxes.
https://www.kingsfund.org.uk/projects/nhs-in-a-nutshell/how-...
National Insurance is also de facto a payroll tax in the UK and a pretty steep one at that it will be over 15% come April if the NIC increases are implemented as is.
That's not saying much since the NHS covers far more than what private insurance does in the US. Furthermore, in the US we have to deal with the absurdities of deductibles, co-insurance and "out of pocket" maxes (private insurance in the US does not kick in 100% until all of these are met). So on top of high monthly premiums, you still wind up with large bills and even larger if you go to a facility that is "out of network". Also dental/eye care are most often separate insurance policies with different companies. I'd take the NHS any day over the asinine system we have here in the US.
Life in London for example is just as expensive if not more than San Francisco/New York. We pay for our national health insurance too and probably comparable to what Americans pay for their private.
People can barely afford an average house/flat as a full-time senior software engineer in UK and are not paid too different than any other office based role.
And no it's not because there is more money in US for tech, because a lot of people in UK work for American companies and I guarantee you they get paid less than their US devs.
American companies outsource their tech to Europe for the sole purpose if being cheap especially to eastern EU countries.