In a society where prostitution were legal, open, and market regulated, this sort of law would make some sense. Under such a regime, most (or nearly all) advertised prostitutes and brothels would, in all likelihood, be legit. Few people trafficking in sex slaves would want the attention that comes with openly advertising their services.
But black markets by definition obscure information from consumers. When prostitution is illegal (or quasi-legal, as it is Britain), it's hard to distinguish voluntary sex workers from involuntary ones, because they're all illegal. They all operate underground. There's undoubtedly a clear moral distinction between patronizing a sex worker who chooses to sell her body, and one who's forced to do perform under the threat of harm by a pimp or a mama-san. The problem is that under a prohibition on prostitution, it becomes more difficult for Johns to make that distinction.
The other sad irony here is that I would guess that all else being equal, most Johns don't want to have sex with a woman against her will. Yes, I'm sure many Johns today practice some willful ignorance about the status of the prostitutes they patronize. But in a society where sex for money were open and legal, the sex slave trade would almost certainly lose a huge chunk of its market share (whatever that may be). Given the option between legal sex with an advertised prostitute or brothel or risking arrest by having sex with a prostitute in a shady, unadvertised, unregulated, underground brothel that may be using sex slaves, I don't think it's wildly speculative to say that most Johns would choose the former.
In any case, under such a scenario, you could certainly make a stronger case for throwing the book at those who choose the latter.
Start your day with Reason. Get a daily brief of the most important stories and trends every weekday morning when you subscribe to Reason Roundup.