The SC said that where services are segregated it has to be by sex. (More widely, wherever sex is mentioned in the EA, it has to be biological.) Toilet provision at work isn't governed by the section of the EA on services at all. Workplaces aren't open to the public or a section of the public, so that section is of no use.
The EA doesn't say you have to provide single sex toilets at work at all. That's in the Workplace Regulations. (We want to say that the definition of men and women carries over via the same reasoning in FWS, but no court has said that, yet.)
The best argument I can find is that the Workplace Regulations should be interpreted biologically, and the existence of those separate regulations means that it is no longer "reasonable" for anyone with the PC of GR to feel dignity-violated by using the correct sex toilet. A => B, as it were.
However the logic is reversible: if A=> B then B' => A' - if we start from the proposition that it is reasonable for anyone with the PC of GR to feel dignity-violated etc. then a biological interpretation of sex in the Workplace Regulations must be incorrect.
You also wrote this:
You may be right, but isn't that a harsh illustration of the different attitudes to the 250,000 transpeople, and 16m disabled people?
'Reasonableness' limits for the 16m, but 'whatever they ask for, everywhere, regardless of cost' for the 250,000.
I think so. The amount of time and attention, and money, that is being devoted to trans issues throws a terribly harsh light on the clear contrast with the way disabled people are considered. It's quite stark, when one turns attention to it.