There are very few suits with which I would not naturally wear brown shoes - a deep, burnished chocolate looks better with everything from navy herringbone to grey check.
But charcoal is an exception. The only other is probably black, which is restricted to evening wear (though the French have a curious fondness for the black suit).
Charcoal brings out little in brown shoes: something about the darkness and simplicity of the colour demands black calf. There is little subtlety or movement to a dark grey suit. Even a mid-grey worsted with little surface detail has variation in tone as it moves which complements a brown shoe, such is its usual patina.
And of course charcoal is just very dark, likely the darkest and most devoid of colour in a man's wardrobe. If one's shoes look best when they are darker than the trousers above them, black is the only option.
This suitability of charcoal and black is particularly true for a flannel suit, as in the illustration above (Ralph Lauren, A/W 2010). The only exception here might be a dark brown suede shoe, perhaps a slip-on, the matching of textures enough to distract from the disparity in colour.
Few men, particularly in London, wear brown shoes well. One recommendation I would have for them is to always wear black shoes with charcoal.