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 inbetweeners.
The Crown
Downton Abbey
Ripper Street
The Royale Family
Shameless
MI-5 ( 10 series)
Ab-Fab
Skins ( 7 series, 61 episodes)
Luther
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)
Grantchester
The Night Manager
Shetland
Midsomer
Morse
Endeavour
Poldark (Aiden Turner)
Vera
Doctor Foster
Misfits
Happy Valley
Torchwood
Life on Mars
Ashes to ashes
Derry Girls
Doc Martin
Auf Wiedersehen Pet
The Office
Being Human
Peep Show
Still Game
Marcella
Bancroft
Prime Suspect
New Tricks
Waking the Dead
Wycliffe
Spooks
Wire in the Blood
Unforgotten
Our Girl
McMafia
Antiques Roadshow
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 )