They use this free housing as their "business premesis".
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.
Others points I believe are correct.
Most HB fraud is criminal gangs using fake id, or individuals who are cohabiting but claiming as singles.
If you operate a cash only business with no paperwork there will always be a temptation to under report earnings.
True it's legal to pay for sex, but it's illegal to offer sex for payment, or to live off immoral earnings.
It's certainly not illegal to respond to an advert offering paid sex or to place such an advert. I have no idea what the law would be regards propositioning people at random.
Edit: Paying for the services of someone who is coerced into prostitution against their will is also illegal.
Source: http://sw5.info/law/punters/
I know. A shocking concept: law has underlying moral values like "it's bad to kill people" and "stealing people's cars is wrong" and so on.