British crime shows (split from Mare of Easttown)
If you're enjoying Mare of Easttown (influenced by British crime shows) or just looking to try something different, the UK offers a wide variety of police/crime/mystery shows. I'll mention some good/bad (personal preference) ones I've seen; hopefully others will chime in.
Babylon - amazing dialogue
The Bay - a police officer and mother tries to keep her household together while solving crime. I found the second series stronger than the first.
Broadchurch seasons 1-2 - great interplay between the two detectives investigating murders
Death in Paradise seasons 1-6, 10 - (Mostly) lighthearted series about a fish out of water UK detective sent to a Caribbean island where he solves crimes. May be problematic for some viewers (white male detective in charge of black officers).
Foyle's War - crime doesn't stop just because there's a War on.
Gangs of London - heard great things about this but haven't seen it yet. Clips on YT indicate the action is amazing.
Grace - only one episode out but strong so far
Line of Duty - internal affairs investigating police corruption. Gets more unbelievable with each new series (like a lot of British crime shows) but has strong material/scenes
Luther - serious (gory) crimes
Marcella - while completely unbelievable, Anna Friel keeps the show interesting as a policewoman with a mental disorder
Prime Suspect - tough policewoman makes her way in a male-dominated force. I found it good until the drug dealer? episode where the quality nosedived.
Sherlock - Holmes and Watson in modern times. I found the show uneven but still entertaining.
Unforgotten - two detectives investigate cold cases. I find the stories pretty meh but the two leads elevate the material
Vexed - comedy
Death in Paradise seasons 7-8 - boring detective
Life of Crime - notable mostly for Haley Atwell as the star
Prime Suspect: Tennison - attempted reboot of classic series
Wild Bill - US police chief moves to UK to becomes a chief constable. Dull except for some interesting characters
Death in Paradise season 9 - show writers badly misjudged the humor this season
Broadchurch season 3 - not just the victim was hit in the back of the head this season, the writers were as well