It's unlikely to be illegal as it's just a training manual - usually the way these things play out is that a manager will rely on the guidance, it gets taken to an employment tribunal and then the guidance will be quietly amended once the lawyers get involved and it becomes clear that it was incorrect advice in the first place. Hopefully I won't get to that stage if we make enough noise about it now, though.
Obviously if the NHS commissioned a third party to write the guidance and the third party did this, the NHS could take it up with them under the commissioning contract. However, here it appears to be presented very much as a collaborative piece between the NHS and the LGBT foundation, so no-one's going to take responsibility for any lies or misinformation.
It's similar to what happened in Sweden where the collaborative medical guidance on transitioning children quoted a high figure for trans kid suicides, but when the documentary makers of The Trans Train investigated the source of the suicide statistics in the report (that doctors were using as their main rationale for medically transitioning children), none of the doctors took responsibility for the inclusion of the stats and one doctor eventually admitted "oh, that's an unfortunate mistake, it was just supposed to refer to mental health issues more generally" (or words to that effect).
That's the trouble with all these collaborative guidance reports being relied on by medical and other professionals in the absence of actual peer-reviewed science and authored reports from actual experts (legal, medical or otherwise) All kinds of batshit hyperbolic claims creep in and no-one checks them as they assume someone else will, and none of the individual authors are worried about their professional reputation or credibility because it's a collaborative piece between several organisations and their individual names aren't anywhere near it.
Also, because the big idea with gender ideology is to listen to trans people and treat them as the experts on themselves, the people putting together this kind of guidance often forget that while the trans person obviously is an expert on how they feel, they might not actually be an expert on the law and might be misquoting a case as that's not the thing they're an expert in. Similar things seem to occur in psychology, etc, where despite psychologists knowing how psychology works, they throw all their training out the window when a trans person says "oh, but that doesn't apply to me as I know how I feel".