It starts a little slow but I ended up really getting in to Adam Dalgliesh. Unfortunately it looks like it’s only on Region 2 
My favorite kind of programming!
Luther - Idris Elba!
Above Suspicion - wish there were more episodes
Rebus - prefer John Hannah in season one, but it’s a good program
Endeavor - agree that it’s better than Inspector Morse
Inspector Lewis - he worked under Morse.
Midsomer Murders - similar in tone to a cozy like Miss Marple. Later seasons decline in quality IMHO
MI-5 is like the British FBI, not police, but it’s one of my favorite programs
Foyle’s War - set in the 1940s. I love this program.
Vera - absolutely superb.
Ripper Street - another period piece, but good mysteries
Touch of Frost - a little dated, but I enjoyed it
Inspector Lynley - I watch them but don’t LOVE them
I’m sure I’ve seen more, but can’t think of the top of my head. I’ve seen a couple set in Scotland, and the dialog takes a bit of getting used to.
It’s British-lite, but check out Murdoch Mysteries, about a detective in the turn-of-the-century Toronto Constabulary. His boss is British, in any case.
I’ve seen a couple of episodes of Murdoch. Good recommendation. I don’t know why I didn’t keep watching as it’s another period piece and I enjoy those.
I should add that I watch most of my British police procedurally on Netflix streaming, which is worth the monthly $ for that programming alone. I also use Amazon Prime Instant Video, so some of the programs I recommend may be from there.
Shut eeet! You’re nicked…
Incidentally, also seek out A Touch of Cloth, a British police-procedural parody that I think is a worthy successor to Police Squad!
I really liked The Last Detective. I had watched it on Netflix streaming, although last I checked it was no longer available, but probably is on DVD.
Murder in Suburbia was pretty good too.
Which are available via Netflix.
MI5 (titled ‘Spooks’ in the UK) is more akin to the British CIA. More James Bond than Gillian Anderson. So perhaps doesn’t fit the OP’s criteria, although it’s great and has a huge body count.
No British police drama set is complete without all series of Prime Suspect with the iconic Helen Mirren.
There’s a new Police black comedy series that’s getting a lot of promotion on UK TV right now, Babylon, with the feature length pilot episode being directed by Danny Boyle (28 Days Later, Slumdog Millionaire, Trainspotting, 127 hours, Olympic Opening ceremony, The Beach) so worth looking out for. Hasn’t yet aired in the UK but it must be very soon.
Is ‘Dempsey and Makepeace’ available on dvd or netflix?
Cheesy, over-the-top, 80s fun. Fish-out-of-water American detective is banished to the London Met for being a bad boy, and ends up partnered to uptight, by-the-book, titled female detective. The two leads ended up married in real life.
I have added a bunch of these to my Amazon Wishlist, thanks dudes!
Might I suggest Midnight Riot and it’s sequels by Ben Aaronovitch?
I loved Wire in the Blood.
I loved this series! I think I watched it on Amazon Instant Video, but I can’t be sure.
Also from AIV, Whitechapel. I think there are 3 seasons and it stars Rupert Penry Jones from MI5. (Who are probably more like the CIA than the FBI, as they are domestic spies that sometimes traipse around outside GB, too).
Any episode with Ben Jones in it is a good episode. 
I have such a crush.
Thanks for mentioning Foyle’s War. Not only do I love seeing the historic aspects, but the title character’s quiet rectitude is just mesmerizing to me.
Replacing Tom Barnaby with John Barnaby has rejuvenated the show somewhat, and the relationship between him and Jones is now more lively.