Judging by the Amazon inventory, most shows started out in low-def (480) for at least a couple of seasons. Then, presumably if the show proved itself with an audience, they authorized HD. Thus the first four seasons of the latest Dr. Who were in low-def, and some shows like Foyle's War, never graduated out of it. Masterpiece Theater seems to be an exception, always in HD, e.g. Downton Abbey.

Low-def original resolution could account for some of the low quality you saw. On top of that, they might've chosen a high level of compression to get by with a narrower and cheaper channel.

How did Downton Abbey look on BBC America? That'd be a good test, given that it was produced in HD. Same with seasons 5+ of Dr. Who.

I've found that downloaded 480 video beats streaming or low-quality broadcast low-def by a mile, so you might consider purchasing the low-def shows you really care about it. It's pretty much DVD quality, which can be upsampled for an HD TV with pretty good results. Low-def episodes tend to be a bit cheaper, with $1.99 the going rate ($2.99 for 720 "HD").