> This doesn't mean that is is free, as my National Insurance contributions are substantial, but that I know that I don't bear any financial risk from going to see a doctor.

In fact, it's more important than that. Because you pay NI upfront, it relieves the feeling of burden that you might otherwise feel towards the NHS, which actually makes you more willing to go to the doctor. This means you're more likely to catch minor things before they become major problems (further reducing NHS costs).