"one in sixty houses in London was a brothel"

Henry Mayhew, in his seminal London Labour and the London Poor (1851), recounts the difficulty of accurately estimating the number of prostitutes in London:

"the Bishop of Exeter asserted the number of prostitutes in London to be 80,000, the City Police stated to Dr. Ryan that it did not exceed 7000 to 8000. About the year 1793 Mr. Colquhoun, a police magistrate, concluded, after tedious investigations, that there were 50,000 prostitutes in this metropolis. At that period the population was one million, and as it is now more than double we may form some idea of the extensive ramifications of this insidious vice." (source)

Another estimate from 1859 comes from O'Daniel's Ins and Outs of London:

"In a police report, I recently noticed a return of four parishes, containing in all, about 12,900 houses, and 70,000 inhabitants. Of the houses, 510 were of ill-fame, and of the inhabitants about 4,000 were prostitutes." (source)