I've heard of these International schools before but it was never made clear how they worked. Do you know if there is a similar kind of thing over here that would allow a kid born in, for arguments sake, Germany to be taught the same curriculum as the English kids but by a German speaking teacher

The British International schools were originally set up overseas.

Have a read of this:- http://en.wikipedia.org/wiki/International_school

The Americans do something similar and are just known as the American School.

 No, never heard of anything along the lines of your German example. As far as I know there are no German schools here, although there is the French Lycee in London for French children and open to anyone wanting to learn in French.  A German child would be taught in English here but could attend a "German" language class if the school had German in their Curriculum.