Traditionally, American TV shows have been shot on 35mm film, and British shows were more likely to be recorded on videotape or shot on 16mm film. Standard video and 16mm film are less able to record color in it's full, saturated lushness like 35mm film can.
American TV productions use a great deal more theatrical lighting than do British productions. This is mostly because 35mm film requires much more light to record clear, in-focus images.
British TV shows tend to use a minimum amount of lighting, opting for a more natural look than that of American Television. American TV employs powerful lighting rigs that wipe out all shadows and create, clear, even illumination throughout a given scene.
British interiors are often shot on video, but exteriors were frequently shot on film. This often resulted in a disjointed look between indoor and outdoor shots.
When PAL--"Phase Alternating Line," which is Europe's standard TV format--is broadcast over an American channel, video appears less sharp and colorful than it would in its native format.
TV production crews on both sides of the Atlantic have access to high-def video now, with 1080 lines of resolution. So differences between the look of American and British TV shows are fading.