She has noted (para. 200) that the Regulations are enacted under the Health and Safety at Work Act (1974) and "The general purpose of the 1974 Act is 5 to secure the health, safety and welfare of persons at work. Section 2 provides that “it is the duty of every employer to ensure, so far as is reasonably practicable, the health, safety and welfare at work of all his employees” (the “general duty”)."
She then notes that the only mention of "propriety" is (as you say) in reference to changing facilities.
She goes on to say that "The secondary purpose of the welfare facilities duty is therefore to provide facilities which are separate “where necessary for reasons of “propriety” (what is morally proper)."
Having set out her stall that propriety is a secondary purpose, she then asserts that the separation of men and women in 20(2) is for propriety only. As you point out, 20(2) doesn't say why men and women's facilities have to be separate; it could be for safety, dignity or any other reasons, but she infers it to be only for propriety. I think that's a challengeable flaw in her reasoning.
She then draws attention to a (in her mind) difference between privacy and propriety. She says that privacy is an Article 8 human right, and that single-user cubicles ensure privacy and therefore are required under 20(1). But propriety is not a human right. ("Moral propriety and bodily privacy are not the same. The first depends upon what is socially acceptable. The second is an inalienable human right.")
Therefore, since 20(2) is concerned with propriety, not privacy, Article 8 rights are not engaged when trying to interpret 20(2).