UK had Z-Cars fro January 1962.
In drama terms, HSB offered quite a lot of ‘new’ but the concept itself wasn’t.
Very few TV shows prior to HSB had to be watched in any particular order. Dallas was one, as it began stylistically as a miniseries. Miniserieses (sp?) like Roots and Holocaust definitely had to be seen in order, but they were over in a month.
Apart from being British, I can’t think of any reason Upstairs Downstairs shouldn’t be considered a serial drama.
Hill Street, ER, Rhoda (although MASH* kind of developed one late into its run), either Branded or Alias Smith and Jones, and probably Space: 1999 or The Invaders.
I wouldn’t count Batman as a serial. It was pitched to ABC as an hour-long show. The network liked the idea, but they didn’t have an hour long slot on their schedule. They had two one-half hour slots on consecutive nights, so that why they had a cliff hanger at the end of the first episode and the escape at the start of the next. It may be similar to a movie serial in that respect but every two episode (or occasionally three) arc was self-contained.
Besides, it wasn’t even a drama. 
Two more sitcoms for your consideration: Soap and Mary Hartman, Mary Hartman drew on serial conventions.
Noe of those (except HSB) apply. Some have serial continuity (like the Invaders before and after Vincent starts working with the anti-alien group), but are not serialized.
Space 1999 especially. You can pick any random episode and it is still stupid whether you’ve seen the previous one or not. 
Don’t forget - HSB wasn’t just serialized. Each episode was one day.
Absolutely not true! In the second season their uniforms changed completely!
And the top-level figure of the Security Chief appeared from nowhere!
On a closed world with limited resources!
Sigh. I did like the spacecraft in that one, though.