I only have hearsay to go on, but why do you think it is wrong?
Others points I believe are correct.
Because housing benefit doesn't work like that. It's idiotic to think that it does.
Most HB fraud is criminal gangs using fake id, or individuals who are cohabiting but claiming as singles.
Huh? I have claimed housing benefit when genuinely unemployed in the past (though not for some years). All they need is proof of address, some form of ID ,a statement of earnings/benefits and details of any dependents etc.
If you operate a cash only business with no paperwork there will always be a temptation to under report earnings.
So yeah, a certain proportion of those who operate cash-only businesses - gardeners, builders, whatever - fraudulently under-report their earnings. A proportion of those will also fraudulently claim benefits, though less than you might think - if you're going to do benefit fraud it makes more sense to do it on a larger scale, you're risking the same penalties and getting more income. But in any case, it's misleading to talk as though this were in any way specific to prostitution.
Both people need to be over the age of 18.
There needs to be no element of coercion. The paying person is guilty of an offence if the sex worker is coerced even if the payer is not aware of any coercion.
There needs to be no trafficking. The UK uses a stricter definition of trafficking, which can include someone voluntarily coming to the UK. It also includes travel within the country.
There's some other stuff too about premises used as brothels and about pimps.
Your comments about use of Housing Benefit are weird and wrong and not worth responding to.