Well how about a non-IT solutiion?
I will state up front that I am a very liberal person. What two people (or more) get up to with their own bodies and their own money is their business, if there is mutual consent. And if somebody charges for a "service" and somebody is willing to pay, so what? That is no different from buying another professional "service", like legal advice.
Now to some practicalities. Prostitutes rent houses and flats, and the owners of those flats turn a blind eye to what goes on within them. Perhaps they are libertarians like me. But the difference is, they are receiving money while turning a blind eye. The landlords are living off immoral earnings, to use that nasty phrase. (Why is banking, or arms manufacturing, not considered immoral?)
So perhaps Harperson, if she really wants to do something about prostitution, should prosecute the landlords for living off immoral earnings. If there is no existing law which does this, I am sure this legislation-hooked government can pass one. The properties could be seized under the Proceeds of Crime Act.
But I think this would be a step too far for Harperson. Big chunks of the central London are still owned by very wealthy aristocrats. Like the Earl of Onslow and the Duke of Westminster, and they let out their properties, almost never sell freeholds, turning their blind eyes towards the tenants. I don't suppose that the Earl or the Duke let their properties personally, of course not. But the money ends up in their pockets. There is no way that Harperson would dare to upset bigwigs like them, even if she wanted to. Instead she tries to cause a ruffle about a lurid web site, because that is a very easy target.
If Harperson has any moral integrity, let's see her go after the really big boys. Otherwise, live and let live.