The UK has a decent track record of making multi-series programmes. Some of them made it to the US and some were adopted and adopted ( with varying degrees of success).
Red Dwarf : 12 series, 72 episodes.
Blake's 7 : 4 series 52 episodes.
Peaky Blinders: 5 series, 30 episodes.
Sherlock ( Cumberbatch et al)
Black Mirror 5 series, 22 episodes.
Merlin 5 series, 65 episodes.
The IT Crowd
Call the midwife
The Royale Family
MI-5 ( 10 series)
Skins ( 7 series, 61 episodes)
Line of Duty (and the little donkey)..mentioned previously.
All Creatures Great and Small
Top Boy ( 3 series, 18 episodes)
Strike (4 series, 11 episodes)
Silent Witness ( 24 series, 212 episodes)
The Night Manager
Poldark (Aiden Turner)
Life on Mars
Ashes to ashes
Auf Wiedersehen Pet
Waking the Dead
Wire in the Blood
Shows such as "Strictly", "GBBO". Not to mention the "soaps".
( probably a lot more as well....https://en.m.wikipedia.org/wiki/List_of ... programmes