Just had another thought - David Tennant. He's DI Alec Hardy in "Broadchurch", of course, which is brilliant, but one of the very first roles he played on TV was as another detective - DI Peter Carlisle - in a series called "Blackpool". It's difficult to categorise the show, because it was part musical, part whodunnit and part comedy, but Tennant was brilliant as were David Morrissey and Sarah Parish; two more of my favourite actors. I imagine the producers of "Broadchurch" were thinking of "Blackpool" when they cast Tennant
It's not everybody's cup of tea (and probably sounds just plain weird from my description) but if you ever get the chance, give it a try.
In a slightly similar vein there's Philip Marlowe in "The Singing Detective". One of my favourite pieces of TV drama, from one of our greatest TV Dramatists, Dennis Potter. Impossible to describe in a few words, and Marlowe isn't really a detective (I don't think 'm giving much away here, because it quickly becomes apparent that he isn't) but quite, quite brilliant. Starring Michael Gambon and Janet Suzman and a stellar supporting cast, including Joanna Whalley as a gorgeous nurse, which gets my vote: who could resist?