As you don't understand the difference between individual choice and discrimination this is my last word on this.
A company or establishment stating "no anything" is illegal and they could be prosecuted under the discrimination act, an escort making a personal choice about who to have sex with is not illegal so not discrimination. They would not be allowed to openly advertise no blacks, no whites, nobody over 60, nobody under 25, nobody overweight or nobody anything else if it were.
The rights of an individual and the rights of companies or establishments are two very different things.
It is clearly completely counterintuitive and indeed surely morally wrong to think that anyone could be compelled to have sex to avoid an accusation of discrimination.
However, in terms of what the Equality Act 2010 says, I think it is actualy something of a grey area.
I do not think it is right to say the Act draws a material disctinction between "the rights of an individual and the rights of companies or establishments". The primary definition of discrimination is in section 13(1) and it draws no distinction between individuals and companies:
"(1)A person (A) discriminates against another (B) if, because of a protected characteristic, A treats B less favourably than A treats or would treat others."
It is then section 29 which provides that "service-providers" cannot disciminate on the grounds of protected characteristics (which include age, race, sex etc):
"29Provision of services, etc.
(1)A person (a “service-provider”) concerned with the provision of a service to the public or a section of the public (for payment or not) must not discriminate against a person requiring the service by not providing the person with the service.
(2)A service-provider (A) must not, in providing the service, discriminate against a person (B)—
(a)as to the terms on which A provides the service to B;
(b)by terminating the provision of the service to B;"
It is quite hard to see how, on its own terms, that would not apply to a sex-worker.
(c)by subjecting B to any other detriment."
I think the answer would be that any court would consider there to be an overarching principle of personal autonomy/ consent in relation to sexual activity, but I am not sure that it is there in the legislation. (For example, there is no relevant provision in the "General Exceptions" in Part 14 (sections 191 et seq).)
And it may be difficult to know how and where the line would be drawn.
For example, a dentist or beauty therapist plainly cannot refuse to see a patient based on race.
The same for a physiotherapist offering sports massages.
What about a "massage therapist" offering a sensual massage without a happy ending?
With a happy ending?
What about an only fans worker- can they block a client on the grounds of race?
As i say, i think the law is unclear (and thus unsatisfactory)