Thanks for the comments so far
JRS, what British shows have you been watching if I may ask?
I have been watching
Wire In The Blood..and watched the first
Prime Suspect last weekend(both are great shows).
Before I have watched
Wycliffe,
Poirot,
Midsummer Murders and
Waking the Dead..mostly from TV, though.
I have to say that UK crime shows are generally much better ones than their American counterparts( There are some good ones there, also..not saying that all are bad

)
I agree. Have you see
Cracker (the awesome UK version with Robbie Coltrane of course, not the short-lived US remake)? It's as good as
Prime Suspect. It had a really great cast, out of the bigger names there was also Christopher Eccleston, and you get to see Robert Carlyle in an early guest starring role, a really memorable one.
Other UK crime shows I'd recommend are
The Vice (with Ken Stott - it was great until he left in the last season),
Trial & Retribution (I think that one is still going),
Silent Witness (comparable to
CSI and
Bones in the sense that it's about a pathologist, though it's much darker),
A Touch of Frost (with David Jason in a serious role - though with some humor thrown in as the quirky lead character).
As for US shows, definitely watch
Homicide: Life on the Street! It's one of the greatest TV dramas ever. But it's not like
CSI at all, it's very realistic. It had a few crossovers with
Law and Order, but it's not formulaic as that show, and it's shot in a moving camera documentary style, similar to
NYPD Blue (both shows started around the same time), and like that show, it's not just about the cases but equally about the cops and their lives, but it's much deeper and darker and better than
NYPD Blue. A lot of people also recommend
The Wire, which is from some of the same creative team - I haven't seen it yet, but it's supposed to be a classic.