London Bridge refers to a woman's panties. When guy makes a woman's "London Bridge fall down", he is making her panties drop to the floor so that they can have sex.
In the song by Fergie of the same name they say, "How come everytime you come around my London Bridge wanna go down?" Which equates to "How come everytime I see you my panties end up on the floor and we end up having sex."
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