Whitechapel is interesting but definitely weird. First season is Ripper, second season is the Kray brothers.
There's also Ripper Street, which is almost entirely not about Jack the Ripper. It's certainly got an atmosphere, though it's usually seedy turn-of-the-century London. The acting is fantastic, with Matthew MacFadyen as the lead.
I enjoyed both Ripper Street and Vera.
Vera is fine, and has a good sense of place. I liked the first couple of seasons of Whitechapel, but one of the later seasons just squicked me out too much.
So many British series to choose from. Here's another - Death in Paradise, about Brit solving murders on the fictional Caribean island of Ste. Marie.
The early seasons of Death in Paradise are funny because the British cop so hates being in the Caribbean. He longs for fog and heavy food and darkness and Fiona Bruce on his telly.
Other series with good senses of place:
Fortitude, starring Stanley Tucci, is a really creepy mystery set in Spitzbergen.
Wallander, with Kenneth Branagh and Tom Hiddleston, in Sweden.
The Tunnel, which is an adaptation of the Danish (and later American) series The Bridge, with the Chunnel standing in for the bridge. The dynamic here is the interplay between the English and French cops.
I'll second the rec for Wallander.
We're halfway through Bodyguard and enjoying it very much. It tends to keep you on the edge of your seat a lot, though, so be prepared for dramatic tension up the wazoo. Keely Hawes is always good and Richard Madden is surprisingly awesome.
I have Procedural Problems: I'm watching last week's The Rookie, and am in the middle of reading an old Michael Connolly book, where they refer to Bosch (out of retirement) as "the oldest boot," and I swear to god, I just thought, "Oh yeah, Castle knows Connolly, right? Maybe that's where they got the idea."
EXCEPT SOME OF THOSE PEOPLE ARE FICTIONAL.