I agree about George Gently, and thankful there are so many seasons on Netflix.
If you search for BBC or British mystery on Netflix, you'll get a good number of results. With a few exceptions for US TV shows, I much prefer the BBC and PBS shows when given a choice. Loved Endeavour and of course this past summer the last season of Lewis. There's also Broadchurch, Wallander (although I prefer the Swedish original series with Krister Henriksson), Sherlock, Hinterland, Grantchester, Top of the Lake, and the Worricker Trilogy (sigh, Bill Nighy) to name a few. I have the PBS channel as a separate channel set up on my Apple TV, although it's frustrating how quickly shows expire.
A couple times a year I'll subscribe to AcornTV for a month to watch what's not yet offered on Netflix. On Netflix, I just watched a couple of comedies, Very British Problems and W1A that were both a hoot.
I love TV and feel that this is where the action is these days and not in movies, although occasionally there's a good movie. Just rented A Bigger Splash with Tilda Swinton and Ralph Fiennes, which I liked quite well.
I'm reading one of Elizabeth George's Inspector Lynley books too (With No One As Witness), and I wish Netflix had more of the Lynley series available.