What are Social Taxes?
In the UK context, these are National Insurance. The fine details vary from one country to another but they all cover a similar range of social benefits including health, unemployment, sickness and retirement benefits. In some countries, certain benefits are not included and it is compulsory to take out private insurance. In other cases, you are allowed to opt out of the state scheme and make payments into a private scheme. Of course, if you opt out, the payment into the private scheme then becomes mandatory.
The UK scheme has the broadest range of coverage for one of the lowest rates of tax so it is a much better deal for Brits than many imagine!
The laws governing social taxes are quite separate from those concerned with income taxes and it is not unusual to find that you end up paying the two taxes in two different countries.
For a British person working outside the UK, it is quite feasible to envisage situations in which you pay income tax in the UK and social taxes elsewhere or vice-versa!
There are a number of bilateral treaties concerning where you can opt to pay social taxes when you are working outside the UK. You can read about those here.