The entirety of the scene was meant to showcase the utter destruction and insanity that has been brought about. The PD employed desaturation to give the entire shot a seemingly dead and dreary look, further embedding the idea that this city is gone, and there's no helping it regain its sanity. The duo behind the production design of this scene are Jim Clay and Geoffrey Kirkland. Ironically, their work before Children of Men included films like Space Jam and Love Actually. Without a doubt, this particular scene was an apology for the utterly awful extreme closeups in the giant advertisement that was Space Jam. (Not a joke, that film was literally a huge ad for Air Jordans.)
Sarcasm aside, the duo undoubtedly put together an extremely tough piece and executed it with finesse. This gruesome scene is the second long cut in the film, being preceded by an earlier scene during a car ride. The camera slowly pans along the interior of the car, drifting in and out, with movements that aren't possible if someone was crawling around the car with a camera. In the beginning of the scene, things are relatively good. The characters are happy and the colors are brighter and significantly more saturated than in the previous scene. However, that quickly changes as the car is rushed by a horde of raiders. The scene ends with the car leaving the cameraman stuck in the middle of the road with the policemen. Again, this scene tasked Clay and Kirkland with spot-on placement of extras, and very time sensitive actions of both actors in the car and outside of the car, as well as spot on actions of the camera itself. The setup of this scene was done with the camera being mounted on a green line threaded through the side windows of the car, being controlled by the cameraman as the scene is executed. As with the scene of the city in uproar, the camera constantly keeps the rule of thirds present while drawing the viewer into the scene with the characters.
For me personally, each one of these scenes makes me feel uneasy. The lack of cuts instills a sense of immersion, making someone watching it feel actual fear and anxiety as if they were sitting in the car with the rest of the characters, or running alongside the main character. I'm not a huge fan of shaky-cam cinematography, and this is one of the only films that executes it well in my opinion. While the camera is shaky at times, it always maintains a constant frame of what is needed to be seen in order to effectively tell the story.