As someone suggested in Q&P it could be James Lee Burke but I don't see how they can compare his character to Morse.
Robicheaux is a hard drinking( although he reforms) ,much married Cajun cop in New Orleans and lives in New Iberia.He has a sidekick named Cletus Purcell who is the very opposite to Lewis and the pair of them are a thorn in the side of the NOPD department .Robicheaux does his own thing and follows his own agendas .And downtown New Orleans is hardly Oxford .
But do read them even if it isn't the one you are looking for . You will be hooked .I have read everything he has ever written .Start with Purple Cane Road.
http://jamesleeburke.com/bibliography.html
However perhaps John Farrow is the one you are looking for . Article
here
where he is compared to Morse