I wouldn't quote it as "the British model" as such. the nordic countries of late have had a big impact esp. stylised.
even the U.S. HBO stuff has had an impact , people still talk about soprano's.. and more recent things like dexter, breaking bad a lot.
there is a cop drama "Line of Duty" that was on for 3 series, that you might like. basically internal affairs and in each series it was "is the main character a dodgy cop or not" scenario.
"The night manager" was decent enough also.
I liked the UK version of "Life on Mars" (thats old now) maybe due to some of the things featured , as it was based in 1973.. the follow on , ashes to ashes I didn't like too much (woman in that is better in line of duty I thought)
there is a UK version of " Wallander" which originally is swedish.
Happy Valley was on a while back and another thing "good cop" which I recall.
http://www.bbc.co.uk/bbcone/programmes/genres/drama/crime/all has a list of things and films that well come under "crime" I guess.
you might want to look into Dr Martin Fido's stuff.. he used to do radio shows in London about famous, sorry infamous folk.. oddly an ex g/f was living years later, on the same road as one of them.
people on the "digital spy" forum are stupidly clued up on this stuff.