Sweden doesn't require them, but vaccinations are both free and optional (but recommended). Without as many people who have decoupled science from life (i.e. they remember that the reason these diseases aren't around any more isn't that we got lucky, it's that we got vaccinated). I don't know if they're required in the UK, but they're certainly recommended.
Remember polio? Probably not, but it was greatly feared. As was smallpox, and plenty of others. Consider that right now Rwanda is having a huge crisis with cholera. We don't require cholera vaccines, because, well, it's not likely here in the US. But we're so very mobile that the possibility of being exposed is way higher than in some other countries.
We tie school attendance to vaccination. Why? Well, because schoolrooms are little incubation chambers; all that exposure to and with people who don't pay a whole lot of attention to hygiene. And they're not required; if you home school your kids, you don't have to vaccinate them. Remember -- freedom isn't free, and all that.
Wendy P.