I know its not British (though Hugh Laurie is) but House is a terrific show that ran for a LONG time. It kind of lost it's luster in later years, but really picked up at the end of it's life, and even follwed in the Sherlockian footsteps of "The Final Problem" if you know what I mean. 

This might seem like a weird suggestion, but the current "Doctor Who" is similar in style and writing (probably because Moffat is the head writer for both shows and Mark Gatiss is a strong contributor).  The characters of the Doctor and Sherlock share many characteristics...both are the most intelligent person in the room, are completely oblivious to how they are perceived by those around them (and don't care about it), are unreadable and both harbor some very dark secrets.  They are also incredibly full of themselves and crave attention...yet are very lonely.  Obviously the tone and storylines of each series differ greatly, but there are some fundamental similarities.  That's probably why both of these shows are m two favorite shows currently.