Here's my quick take on this. Women of the upper class sometimes found themselves pregnant when they didn't want to be, and Mrs. Grimston, whoever he or she was, would attempt an abortion. It's interesting that the ad is so prominently headed. Le Beau Monde was directed toward the upper class or at least the mid-to upper class.
Ladies in this situation (under peculiar circumstances) may obtain a confidential Friend, and secure their honor and happiness, by addressing a letter (post paid) to Mrs. Grimston, No. 18, Broad-street, Golden Square, London, when a private interview with the Advertiser will be appointed.