A list of British shows (on-going series, not short, closed-ended "mini-series") I've liked over the years...worth recommending...
Sherlock (latest version)...nicely modern version
Prime Suspect
Silent Witness
Inspector Morse...a great character followed up successfully by...
Endeavor, Morse's beginnings and
Inspector Lewis, Morse's partner continues the series
Psycho-dramas more than mere procedurals
Touching Evil
Wire in the Blood
Cracker
Wallander...the drama is in Wallander's psyche.
Luther
Inspector Alleyn Mysteries
Inspector Lynley Mysteries
Cadfael..because of Derek Jacobi
Foyle's War because of Michael Kitchen
One American show of many...
In Plain Sight
God, I've watched too much TV...