AMC and HBO aren't broadcast over here because they're subscription only channels.
Subscription channels aren't bound by service remits and so can put a portion of their cash into quality drama and comedy programming, and don't have to worry about meeting a diverse range of audiences.
The downside to that is, and what many British viewers are unaware of because we only see the good stuff, is that in between those great shows channels like HBO, AMC and Showtime fill up their broadcast hours with reality TV, films, softcore porn and sport. Oh and repeats. They repeat their top shows on a daily basis.
Still, it's that subscription service which allows them to deliver high quality series'.