The original can. Either can go in several locations depending on your mood.
IMDB lists the genres for The Avengers as: Action | Comedy | Crime | Mystery | Sci-Fi | Thriller and The New Avengers as Action | Mystery | Thriller.
Those "films" in the LOTSW "Pink set" are actually the 1983 Christmas Special (Disc 1) which follows series 7, and the first 3 episodes of series 1 edited together to make a "feature film" (Disc 2). Disc 4 of that set is the 2nd half of series 1 and Disc 3 is the first 3...
First some to add:
Robin of Sherwood (entire series - Acorn Media [OOP])
Lovejoy (entire series - BBC [OOP]/Acorn Media [in progress])
Poirot (entire series - A&E and Acorn Media [OOP]/Acorn Media [remastered in original air order])
Cracker (entire series - HBO...