And in America we use "series" to refer to the complete series. You bloody Brits need to keep up with the lingo! :)
More seriously, I think it has to do with the fact that once upon a time a new season referred to the fall specifically, to time the start of new episodes with when car companies began marketing their new models (in September). "Fall season" just became a "season" of a show, and that stuck even as new shows can potentially start at pretty much any time of the year.
I can't imagine how they wound up being called series in Britain though.