London, like every other large city, breaks down into a large number of districts, each with its own character and dangers, so much would depend on who you were - meaning what social class you came from - and where exactly you were wandering, at what time of day.

However, we can say that, in general, while the West End was relatively high class, well policed and safe, much of the rest the city was certainly not absolutely safe, and some parts of it - specifically the area south of the river, in Southwark, and much of the East End - were relatively unsafe. Even so, it's certainly not the case that you would have had a high chance in this period of being physically attacked, robbed or murdered on the average London street if you had simply wandered down that street once. In fact, by far the most likely outcome of being a single woman out on the streets alone in this period would be that you would be mistaken for a prostitute and propositioned for sex. Women from the upper and middle classes who were past the age of puberty and unmarried simply did not go about unchaperoned at any point in this period, and - as I commented in a previous answer on a related topic - for the most part lived extremely restricted lives at home. So the general presumption was that single women would be working class and, if not clearly engaged on some specific task, would be sex workers loitering in the hope of attracting clients.

There is an extensive literature on women and the city in the Victorian period, much of it focused on the "dangers" and "lures" of the town rather than the opportunities and entertainments it offered. A good place to start would be Judith Walkowitz's influential City of Dreadful Delight: Narratives of Sexual Danger in Late Victorian London (1992).