There is no single piece of legislation covering sex work and/or prostitution in the UK. Governing law arises from a multitude of sources and often archaic and idiosyncratic case law. We try to cover important points here, without claiming comprehensive coverage. Prostitution itself is legal in the UK, however a multitude of related offences mean that sex workers and clients have to be particularly astute in order to not fall foul of related laws.
Prostitution is defined by Sexual Offences Act 2003 51(2) as
“a person (A) who, on at least one occasion and whether or not compelled to do so, offers or provides sexual services to another person in return for payment or a promise of payment to A or a third person; and “prostitution” is to be interpreted accordingly.”
The definition is given for the purposes of the act, though the definition may be used elsewhere. It does not appear to mandate sexual intercourse
Sexual Offences Act 1956 section 33 makes an offence of keeping managing or assisting in managing a brothel. Subsequent sections criminalise landlords and tenants allowing a premise to be used as such. The act itself does not define the term brothel, the CPS guidelines provide a definition as “a place where people of opposite sexes (see paragraph below) are allowed to resort for illicit intercourse, whether the women are common prostitutes or not”  referring to earlier case law (Winter v Woolfe ). The Sexual Offences Act 1967 extends coverage to homosexual acts.
It remains the management of the brothel (not offering sexual services from a brothel) that constitutes the offence, though sex workers may be identified as also managing the premises.
Stevens v Christy  identifies that two or more women (presumably also interpretable as men) work as prostitutes from a premises (even at different times) then it may be considered a brothel.
Advertising for sexual services by placing an advert in a public telephone box was made a specific offence by the Criminal Justice and Police Act 2001. Advertising in other locations is not illegal, though the CPS guidance advises that prosecution under the Proceeds Of Crime Act 2002 may be possible (but does not elaborate in detail).
Living off immoral earnings
This is defined by the Sexual Offences Act 1956 as
(1)It is an offence for a man knowingly to live wholly or in part on the earnings of prostitution.
(2)For the purposes of this section a man who lives with or is habitually in the company of a prostitute, or who exercises control, direction or influence over a prostitute’s movements in a way which shows he is aiding, abetting or compelling her prostitution with others, shall be presumed to be knowingly living on the earnings of prostitution, unless he proves the contrary.
Whilst the law can be interpreted as targeting those controlling sex workers (aka pimping), it might also be equally applied to the partners of sex workers who do not demonstrably have their own income.
Paying for sexual services from someone subject to force
The Sexual Offences Act 2003 section 53A makes it an offence to pay for sex from someone who has been coerced. Whilst Backlash is only concerned with consensual acts, the SOA is explicit in stating that;
(2)The following are irrelevant—
(b)whether A is, or ought to be, aware that C has engaged in exploitative conduct.
which criminalises behaviour based on events unknown and possibly unknowable to an individual – their reasonable belief being that the activity is consensual. The act creates a strict liability offence in which a person can be criminalised for an activity which to the best of their knowledge is legal. “A”, above may take any measure to discover that the person they are paying for a sexual service is not coerced and still remain criminally liable if they fail to discover that coercion is present.
Soliciting, Loitering and nuisance.
Soliciting for sexual services in a public place is an offence under the Sexual Offences Act 2003, as is the somewhat reciprocal, soliciting to provide sexual services, defined by the Street Offences Act 1959.
 The bracketed (see paragraph below) part is inside a verbatim quote on the CPS website, probably erroneously.