Have a look at the images below and tell me why all these landscapes are so blurred? What can be the motive behind doing that? The blurred part is mostly at the top half of the images.
BCdotWEB's answer does an excellent job of explaining how this effect is done, and I just wanted to chime in a little about a possible why.
Tilt-shift is used to make real life, full-sized landscapes look like miniature models: people appear as dolls, massive buildings become nothing more than toys. A major theme throughout the Sherlock BBC series is how Sherlock's incredible analytical mind leaves him struggling to relate to others as fellow humans rather than puzzles to be solved, and his analytical skills often takes him into conflict with larger-than-life villains (such as Moriarty) who openly view other humans as nothing more than toys to play with and discard.
Looking at the series through this lens, the tilt shift effect turning London into a model set filled with living dolls can be interpreted as a way to metaphorically show the city through the perspective of the geniuses, good and evil, who the series revolves around.
Tilt-shift photography is a creative and unique type of photography in which the camera is manipulated so that a life-sized location or subject looks like a miniature-scale model. Essentially, it’s taking a photograph of a real-world scene and making it look like a miniature scene, such as you’d find in a model railroader’s setup. This, as shown above, was used in the opening credits of Sherlock, along with other shots of London. Tilt shift photography can be done with the help of a lens which is capable of tilting and shifting or, more usually, it can easily be processed in Photoshop almost under a minute by people who are experienced with this process.
Tilt shift lenses allow the lens to be tilted at an angle tho the focal plane – normal lenses are parallel to the focal plane. This creates the unusual effect of an apparent shallow depth of field where there wouldn’t normally be one. In practical terms – tilt shift images look like miniatures or models. This happens because we are conditioned by our familiarity with miniature macro photography and its inherent shallow depth of field.
Here is someone who recreated it using stock footage:
It's definitely on purpose. Being an artistic choice, I can only speculate on the "why," but I do have a guess.
Tilt-shift creates a miniature effect, an interesting way to represent how Sherlock stands over the petty concerns of mere mortals. We scurry about, our boring lives as monotonous to him as the spinning of a hamster wheel, and he captures it all with his godlike intellect.