I am really enjoying listening to the Jackie Faber series.  It is set in the early 1800's in London, at least the first book is set in London.  The main character is a young (12-15) year old girl who begins the series as an orphan.  It is the tales and adventures of her life and she does get herself into some pretty interesting scrapes.  I am on book 5 and each book has some of the same cast, but are totally different plots.  Highly recommend if you like YA novels.

Here is a blurb from Goodreads

Bloody Jack (Bloody Jack, #1) 4.21  ·  rating details  ·  2,579 ratings  ·  539 reviews

Life as a ship's boy aboard HMS Dolphin is a dream come true for Jacky Faber. Gone are the days of scavenging for food and fighting for survival on the streets of eighteenth-century London. Instead, Jacky is becoming a skilled and respected sailor as the crew pursues pirates on the high seas.

There's only one problem: Jacky is a girl. And she will have to use every bit of her spirit, wit, and courage to keep the crew from discovering her secret. This could be the adventure of her life -- if only she doesn't get caught....