The healthcare is not free, it's paid for by taxes. International students are not covered.

You will need to have your own coverage that is valid in the country that you are in.

I was planning on studying abroad over in a European country, most likely the UK. If I become ill or anything and need to see a doctor or go to the hospital while I'm over there, how will their healthcare system work for me, or any international student? I'm from Hawaii.