I was wondering, what was the average cost of a London prostitute in 1888? Do we have any accounts of the average per time fee and per week income? How did this vary across the UK? I'm also wondering, what amount did the illegal prostitutuon business contribute to the UK economy?
I can only address your last question, and only to a degree. The illegality of prostitution in Victorian England was not codified into law until the 1885 Criminal Law Amendment Act. Prior to 1885, there was quite a bit of legislative turmoil around the subject of prostitution.
The rise of the middle class in the mid 1800's led to the rise in the middle class moralistic idea that prostitution was a social evil that must be combated with laws restricting the practice. It's much more complex than that, but we're just talking about selling sex- Victorian views on sex are an entirely more complex animal.
The proposed Brothels Suppression Bill of 1840 attempted to place regulations for the "Suppression of Bawdy Houses, and of the Trading in Seduction and Prostitution." It ultimately failed in part due to some sitting Lords expressing fears that "any attempt to put such houses down by summary means would only lead to their transfer and re-establishment in other parts of the town, at present free from such nuisances."
A similar bill, Protection of Females, failed in 1848. This bill was opposed in part because some Lords opposed regulation of prostitution on economic grounds- a sort of "free market" concept.
Parliament then passed the Contagious Diseases Acts of 1864, 1866, and 1869, which officially allowed prostitution in almost a dozen military towns, with the contingency of requiring the forcible examination of prostitutes (and any remotely suspicious-looking working class woman in the area) for disease. If a woman was found to be suffering from a venereal disease she was placed in a locked hospital. The purpose for this act was to protect sailors from diseases. Naturally, this provision did not sit well with emerging women's rights activists who viewed prostitution as a form of slavery.
Prostitution (and re-criminalized male homosexuality) was made illegal in 1885 and the CD Act was repealed in 1886.
As far as accounts of actual prostitutes, in July 1885, the Pall Mall Gazette published a series of articles, “The Maiden Tribute of Modern Babylon, ” which described how its editor, W. T. Stead, arranged for the purchase of thirteen-year old Eliza Armstrong for five pounds from her alcoholic mother, with the mother’s full consent that the girl would be put in a brothel.