As much as I like the Reincarnation AU ideas I’ve seen posted, I don’t think Jack Armstrong(from Vexed) and Joe Chandler (from Whitechapel) would make a good pairing, in spite of being policemen and such. Jack would drive Joe crazy. Literally.
Not to mentiom that in one episode Jack uses a guy with OCD to clean his house for free. Imagine poor Joe
However, Jack and Clive (from Silk)… that would be a good couple. The policeman and the barrister.