St. Albans School
So, you St. Albans is older, has more illustrious graduates, and is more prestigious; huzzah. My feeling is that the American St. Albans has the unqualified name because it has been around on Wikipedia for much longer - almost a year. Also, Wikipedia stared as a primarily American project, so it makes a little sense that it would go first. So I guess I'm saying in a complicated and sarcastic way that I support the move, with a disambiguation page. After all, both schools have a good relationship and participate in an exchange. 

PS, There is also high school in St. Albans, Vermont, although I'm not sure after whom it is named.