Yes, there are 6 different regions. While it is possible to change the region of many DVD players, the player will not play American DVDs if you change it from Region 1, which is the US/Canada region.
I know this because my mom used to have the entire German set of the Bonanza TV series. We had to change our PC's region to Region 2 (Europe) to play them. Once we did, I could no longer play my movies on my computer, which was a bummer.
Your best bet for Detectorists and other British shows is to purchase the seasons digitally, or double-check that the DVDs you buy are designated Region 1, like these:
https://www.amazon.com/Detectorists-Mackenzie-Crook/dp/B00VKX6VWC
I almost made the same mistake when purchasing Monty Python's Life of Brian for myself. I could only find one pack that included both Life of Brian and The Holy Grail, but it was a British release (Region 2).
As for the OP, I am very excited to hear that they will be bringing Detectorists back for a third season (although I haven't even finished the second season yet- I don't have Netflix). There is something about British humor that is very appealing.