London Fog vs. Light
Symbolism, Imagery, Allegory
Not Just a Raincoat
The London fog serves to shroud or veil the city and make it eerie. Fog = obscurity, and the literal fog emphasizes the metaphorical fog surrounding the true identity of Hyde:
A maid servant living alone in a house not far from the river, had gone upstairs to bed about eleven. Although a fog rolled over the city in the small hours, the early part of the night was cloudless, and the lane, which the maid's window overlooked, was brilliantly lit by the full moon. It seems she was romantically given, for she sat down upon her box, which stood immediately under the window, and fell into a dream of musing. Never (she used to say, with streaming tears, when she narrated that experience), never had she felt more at peace with all men or thought more kindly of the world. (4.1)
The weather patterns of London seem perfectly suited to dastardly deeds done dirt cheap. Although there is "brilliant" moonlight early in the evening (which makes the maid feel at peace with all mankind), a really ominous fog rolls in when all hell is about to break loose.
You've also got firelight, lighted lamps, and light in general as the counterpoint to fog because of their safe, illuminating qualities.